Geometry B-5, Geometry Ch. 4, Geometry Ch. 3, Geometry Ch. 2

Hexagon DEFGHI is translated 8 units down and 3 units to the right. If the coordinates of the pre-image of point F are (-9, 2), what are the coordinates of F'?

(-6, -6)

Which point is on the line that passes through point H and is perpendicular to line FG?

(-6, 10)

What is the pre-image of vertex A' if the image shown on the graph was created by a reflection across the y-axis?

(-6, 8)

Rectangle EFGH is translated according to the rule T-5, 9(x, y). If the coordinates of the pre-image of point H are (-2, -3), what are the coordinates of H'?

(-7, 6)

In triangle ABC, BG = 24 mm. What is the length of segment GE?

12

What is the order of rotational symmetry for a rhombus?

2

Point X is the circumcenter of ΔABC. What is the length of MB?

2.5 cm

Point Z is the circumcenter of ΔTUV. What is mZUB?

32.8

What is the minimum angle of rotational symmetry for the quadrilateral shown below?

360

Given the information in the diagram, which theorem best justifies why lines e and f must be parallel?

72/ 108 converse of the same side interior angles theorem

Consider the transformation shown. Which angle corresponds to N?

<N'

Lee is creating a garden with the dimensions shown. He creates paths through the garden along AB, XY, YZ and . Which correctly compares the lengths of the paths?

A

Which statement best explains the relationship between lines PQ and RS?

They are not parallel because their slopes are not equal.

Consider the diagram. Why are lines e and c skew lines?

They lie in different planes and will never intersect.

A transformation of rectangle LMNO results in rectangle L'M'N'O'. Which transformation maps the pre-image to the image?

stretch

Which figure represents the image of trapezoid LMNP after a reflection across the x-axis?

figure A

A composition of transformations maps ΔXYZ to ΔX"Y"Z". The first transformation for this composition is______ , and the second transformation is a 90° rotation about point X'.

a reflection across line m

What is the final transformation in the composition of transformations that maps pre-image GHJK to image G'H"J"K"?

a reflection across line m

In the diagram shown, the distance between points A and C is the same as the distance between points B and G. Lines AB and CG are

parallel

Consider the diagram. Lines a and d are

perpendicular.

Complete the statement about the transformation. Point F' corresponds to

point F

Consider the two rectangles shown. A_____ maps rectangle QRST to rectangle Q'R'S'T'.

reflection

Triangle ABC is congruent to A'BC' by the HL theorem. What single rigid transformation maps ABC onto A'BC'?

reflection

What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?

x + 2y = 8

Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures?

ΔDEF ≅ ΔSRU

Figure ABCD was reflected across the x-axis to create figure A'B'C'D'. What are the coordinates of the pre-image of B'?

(-8, -2)

Which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB?

(0, 2)

If a translation of (x, y) → (x + 6, y - 10) is applied to figure ABCD, what are the coordinates of D'?

(1, -12)

Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?

(1,0)

Triangle TRS is rotated about point X, resulting in triangle BAC. If AB = 10 ft, AC = 14 ft, and BC = 20 ft, what is RS?

14

In the diagram, TQ is 18 units in length. What is the length of RS?

25 units

Lines a and b are parallel and lines e and f are parallel. If m∠1 = 89°, what is the measure of ∠5? m∠5 =

91

The rule as a mapping for the translation of a rectangle is (x, y) → (x - 2, y + 7). Which describes this translation?

a translation of 2 units to the left and 7 units up

An orthocenter is the intersection of three

altitudes in a triangle.

Which new angle is created by extending one side of a triangle?

an exterior angle

Which statement is true regarding triangle TUV?

Angle V is the smallest angle.

Which points lie on the line that passes through point P and is parallel to the given line? Check all that apply.

(-1, 3) (-2, 2) (-5, -1)

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)?

XX a: y + 3 = −4(x + 4)

The rule ry-axis • RO, 90°(x, y) is applied to ΔABC. Which triangle shows the final image?

1

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.

XX 2x + 5y = −10 y + 4 = -(x - 5) for sure B

The value of x is (130, 134)

XX 86

Which shows the image of quadrilateral ABCD after the transformation R0, 90°?

XX d

Which statement regarding the diagram is true?

XX m∠JKM + m∠MLK = 180°

What is the equation, in slope-intercept form, of the line that is perpendicular to the line y - 4 = -(x - 6) and passes through the point (−2, −2)?

d: y =3/2 x + 1

Lines e and f are parallel. The m9 = 80° and m5 = 55°. Which angle measures are correct? Check all that apply.

m2 = 125° m8 = 55° m14 = 100° m16 = 80°

Lines b and c are parallel. What is the measure of 2?

m2 = 50°

The m6 = (11x + 8)° and m7 = (12x - 4)° What is the measure of 4?

m4 = 40°

A line has a slope of . Which ordered pairs could be points on a line that is perpendicular to this line? Check all that apply.

(-3, 4) and (2, 0) (1, -1) and (6, -5)

Which point is on the line that passes through point R and is perpendicular to line PQ?

(-4, -8)

A triangle has vertices at R(1, 1), S(-2, -4), and T(-3, -3). The triangle is transformed according to the rule R0, 270°. What are the coordinates of S'?

(-4, 2)

Parallelogram F"G"H"J" is the final image after the rule ry-axis • T1,2(x, y) was applied to parallelogram FGHJ. What are the coordinates of vertex F of parallelogram FGHJ?

(-4, 2)

What are the coordinates of the image of vertex G after a reflection across the line y = x?

(-5, 4)

Square ABCD was translated using the rule (x, y) → (x - 4, y + 15) to form A'B'C'D'. What are the coordinates of point D in the pre-image if the coordinates of point D' in the image are (9, -8)?

(13, -23)

Which point on the x-axis lies on the line that passes through point C and is parallel to line AB?

(2, 0)

Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?

(3, 2)

What are the coordinates of the image of vertex R after a reflection across the y-axis?

(3, 4)

What are the coordinates of the image of vertex D after a reflection across the x-axis?

(5, 3)

Triangle ABC is translated according to the rule (x, y) → (x + 2, y - 8). If the coordinates of the pre-image of point B are (4, -5), what are the coordinates of B'?

(6, -13)

A pentagon is transformed according to the rule R0, 180°. Which is another way to state the transformation?

(x, y) → (-x, -y)

A triangle is rotated 90° about the origin. Which rule describes the transformation?

(x, y) → (-y, x)

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

(x, y) → (x - 3, y + 5)

A triangle on a coordinate plane is translated according to the rule T-3, 5(x, y). Which is another way to write this rule?

(x, y) → (x - 3, y + 5)

A triangle on a coordinate plane is translated according to the rule T-8, 4(x, y). Which is another way to write this rule?

(x, y) → (x - 8, y + 4)

Parallelogram ABCD is rotated to create image A'B'C'D'. Which rule describes the transformation?

(x, y) → (y, -x)

Which statements must be true about the image of ΔMNP after a reflection across ? Check all that apply.

- The image will be congruent to ΔMNP. - EG will be perpendicular to the line segments connecting the corresponding vertices. - The line segments connecting corresponding vertices will all be parallel to each other.

A given line has the equation 10x + 2y = −2. What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( _____ )x + 12

-5

Parallel lines e and f are cut by transversal b. What is the value of y?

130

In the diagram, the length of segment TR can be represented by 5x - 4. What is the length of segment VS?

15 units

Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side at point M. What is the length of MC?

16 mm

What must be the value of x so that lines c and d are parallel lines cut by transversal p?

18

If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?

20

In the diagram, ΔPMN ≅ ΔQSR. If QR = 20 in., RS = 7 in., and SQ = 24 in., what is PN?

20

What must be the value of x so that lines a and b are parallel lines cut by transversal f? The value of x is

22

How many lines of reflectional symmetry does an equilateral triangle have?

3

In the diagram, the length of segment TQ is 40 units. What is the length of segment QV?

44 units

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

4x < h < 10x

Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x - 1) units. What is AF?

51 units

Two parallel lines are crossed by a transversal. If m6 = 123.5°, then m1 is

56.5

Point H is the midpoint of side FK. For the triangles to be congruent by SSS, what must be the value of x? x=____

6

The image of parallelogram PQRS after a reflection across is parallelogram P'Q'R'S'. If RR' = 12, then RZ =

6

In the diagram, g ∥ h, m∠1 = (4x + 36)°, and m∠2 = (3x - 3)°. What is the measure of ∠3?

60

Triangle DEF is isosceles, where . Angle D is bisected by segment DG, creating angle GDE with a measure of 29°. What is the measure of angle DFE?

64

In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet. What is RS?

7 feet

A regular polygon has 15 sides. Which is a possible angle of rotational symmetry for the figure?

72

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

72

Lines a and b are parallel and lines e and f are parallel. What is the value of x?

82

Consider the diagram. What is the length of segment AB?

9

Which of these triangle pairs can be mapped to each other using a single reflection?

A

Which shows two triangles that are congruent by AAS?

A

Consider the triangles shown. If mUTV < mUTS < mSTR, which statement is true?

A: VU < US < SR by the hinge theorem.

The proof ABC ≅ DCB that is shown. Given: A ≅ D; CD||AB Prove: ABC ≅ DCB What is the missing reason in the proof?

AAS

Which statement regarding the interior and exterior angles of a triangle is true?

An exterior angle is supplementary to the adjacent interior angle.

ΔA'B'C' was constructed using ΔABC and line segment EH. For the transformation to be a reflection, which statements must be true? Check all that apply.

BD = DB' CG = GC' m∠EFA = 90° The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.

What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

C: y = 4/3x - 8

Quinton tried to transform triangle FGH according to the rule (x, y) → (-y, x). Which best describes his attempt?

Correct. He transformed the triangle according to the rule (x, y) → (-y, x).

Which of these triangle pairs can be mapped to each other using a single translation?

D

Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?

D

What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?

D 4x + 3y = −6

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?

D: y - 1=3/2 (x + 3)

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)?

D: y = 3x − 5

Which letter in the word HAPPY has an order 2 rotational symmetry?

H

Triangle ABC was translated to form A'B'C'. Which describes the transformation? Check all that apply.

It is rigid. It is isometric. The size is preserved

Which rule describes the composition of transformations that maps ΔABC to ΔA"B'C"?

RB', 270° • rm

The image of trapezoid PQRS after a reflection across is trapezoid P'Q'R'S'. What is the relationship between RR' and SS'?

RR' || SS'

Rectangle ABCD has vertices A(-6, -2), B(-3, -2), C(-3. -6), and D(-6, -6). The rectangle is translated so that the coordinates of the image are A'(-10, 1), B'(-7,1), C'(-7, -3), and D'(-10, -3). Which rule was used to translate the image?

T-4, 3(x, y)

Triangle EFG has vertices E(-3, 4), F(-5, -1), and G(1, 1). The triangle is translated so that the coordinates of the image are E'(-1, 0), F'(-3, -5), and G'(3, -3). Which rule was used to translate the image?

T2, -4(x, y)

Triangle STV is transformed to create the image, triangle UTV. Which side in the image corresponds to TV in the pre-image?

TV

If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?

The figure must be a rhombus because it has exactly 2 pairs of congruent angles.

How are lines KL and MN related?

The lines are perpendicular.

Parallelogram ABCD is rotated to create image A'B'C'D'. Which rule describes the transformation?

XX (x, y) → (x, -y)

Three figures exist such that ABCD ≅ GHIJ and BCDA ≅ RSTU. If GH = 6 cm, HI = 8 cm, IJ = 10 cm, and GJ = 9 cm, what is TS?

XX 8 cm

The figure shows a circle inscribed in a triangle. To construct the inscribed circle, angle bisectors were first constructed at each angle of the triangle. Which happened next?

XX A circle was constructed using the intersection of the angle bisectors as the center of the circle and the obtuse vertex as a point on the circumference of the circle.

How can a regular hexagon be folded to show that it has reflectional symmetry?

XX Fold the hexagon along a line from a vertex to the midpoint of an opposite side. Fold the hexagon along a line connecting the two midpoints of adjacent sides.

Which lines are parallel? Justify your answer. 110\110 80

XX Lines e and f are parallel because their same side exterior angles are supplementary.

One vertex of a polygon is located at (3, -2). After a rotation, the vertex is located at (2, 3). Which transformations could have taken place? Check all that apply.

XX R0, 90° R0, -90°

One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0). Which transformations could have taken place? Check all that apply.

XX R0, 90° R0, -90° xx R0, 90° R0, 180° R0, -90°

Irina wants to tile her floor using the translation shown below. Which is the rule for this translation?

XX T-2, 3(x, y)

Which statements are true about triangle ABC and its translated image, A'B'C'? Check all that apply.

XX The rule for the translation can be written as T-5, 3(x, y). Triangle ABC has been translated 3 units to the right and 5 units down.

Two rigid transformations are used to map ΔABC to ΔXYZ. The first is a translation of vertex A to vertex X. What is the second transformation?

XX a reflection across the line containing AC try a

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)?

XX a: y = -5/2x + 5 try D

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

XX b

Which shows the image of ΔRST after the rotation (x, y) → (y, -x)?

XX b

Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y - 3.5) to create the image ΔA'B'C' shown on the coordinate plane. Which graph shows the pre-image, ΔABC?

XX b a

What is the equation of the line that is parallel to the given line and has an x-intercept of -3?

XX c: y = -3/2x + 3

Which of these triangle pairs can be mapped to each other using two reflections?

XX d

Which type of triangle will always have exactly 1-fold reflectional symmetry?

XX obtuse triangle

What is the equation of the line that is perpendicular to the given line and passes through the point (2, 6)?

XX y = 2 y = 6

What is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

XX y = 5x + 5

Which angle has a measure equal to the sum of the m∠SQR and the m∠QRS?

XX ∠SRE

A composition of transformations maps ΔKLM to ΔK"L"M". The first transformation for this composition is_________ , and the second transformation is a translation down and to the right.

a 270 rotation around p

Two parallel lines are crossed by a transversal. What is the value of a?

a = 63 ( a \ 63)

In the triangles, HG = MP and GK = PN. Which statement about the sides and angles is true?

a: mG > mP

Consider the triangle. The measures of the angles of the triangle are 32°, 53°, 95°. Based on the side lengths, what are the measures of each angle?

b: mA = 32°, mB = 53°, mC = 95°

In the triangles, BC=RS and AC=TS. If RT is greater than BA, which correctly compares angles C and S

b: mC < mS

Which figure shows a line of reflectional symmetry for the letter T?

c

Which shows the pre-image of quadrilateral W'X'Y'Z' before the figure was rotated according to the rule (x, y) → (-x, -y)?

c

Given: g ∥ h and ∠2 ≅ ∠3 Prove: e ∥ f 5. e || f 5. ? What is the missing reason in the proof?

converse alternate interior angles theorem

Given: Lines a and b are parallel and line c is a transversal. Prove: 2 is supplementary to 8 What is the missing reason in the proof? 2?

corresponding angles theorem

Which diagram shows lines that must be parallel lines cut by a transversal?

d

Letters a, b, c, and d are angle measures. Which should equal 105° to prove that f ∥ g?

d (75)

Which type of triangle will always have a perpendicular bisector that is also an angle bisector?

equilateral

Two parallel lines are crossed by a transversal. What is the value of h?

h = 60 (120 \ h)

Which line is perpendicular to a line that has a slope of ?

line LM

Two parallel lines, e and f, are crossed by two transversals. What is the measure of 15?

m15 = 97°

Which figure has the same order of rotational symmetry as a rectangle?

rhombus

Which rule describes the composition of transformations that maps figure PQRS to figure P"Q'R"S"?

rl • RQ, 180°

Which transformation maps quadrilateral EFGH to quadrilateral QRSP?

rotation

What is the rule for the reflection?

rx-axis(x, y) → (x, -y)

What is the rule for the reflection?

ry-axis(x, y) → (-x, y)

Given: m || n and p is a transversal Prove: m2 = m7 What is the missing reason in the proof? 6?

transitive property

Triangle ABC was transformed to create triangle DEF. Which statement is true regarding the side in the image that corresponds to BA?

ED corresponds to BA because they are in the same position.

Cedric applied the rule rm • RP, 90°(x, y) to figure WXYZ. What mistakes did he make? Check all that apply.

He applied the reflection to the pre-image first. He used an incorrect angle of rotation around point P.

Jace is making a water play table from a triangular table top. He sketched a dotted line to show where he wants to add a circular water bowl. It should go all the way to the edges of the table as shown. What should Jace do first to find the exact location of the center of the circular water bowl?

He should bisect each of the angles at the vertices of the triangular table top

If triangle DEF has a 90° angle at vertex E, which statements are true? Check all that apply.

The angle at vertex D is acute. Triangle DEF is a right triangle.

Which statement best explains the relationship between lines AB and CD?

They are parallel because their slopes are equal

Planes T and X are parallel. Plane T contains line a. Plane X contains line b. Which best explains the relationship between lines a and b?

They are skew and will never intersect.

Triangle 1 undergoes four different transformations. The results of these transformations are shown. Which statement best describes one of these transformations?

Triangle 1 is rotated to result in triangle 2.

Square A"B"C"D" is the final image after the rule T-4, -1 • RO, 90°(x, y) was applied to square ABCD. What are the coordinates of vertex A of square ABCD?

XX (-1, -6)

Which triangle has 0 reflectional symmetries?

a

What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B'C"D"?

a 270° rotation about point B'

A point has the coordinates (m, 0) and m ≠ 0. Which reflection of the point will produce an image located at (0, -m)?

a reflection of the point across the line y = -x

A point has the coordinates (0, k). Which reflection of the point will produce an image at the same coordinates, (0, k)?

a reflection of the point across the y-axis

Which statements about the diagram are true? Check all that apply. (DFE 4,9)

a, c, e

Two parallel lines are crossed by a transversal. What is the value of b?

b = 128

Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?

converse alternate exterior angles theorem

What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?

d: y = 4x + 16

Which figure has an order 3 rotational symmetry?

equilateral triangle

Two parallel lines are crossed by a transversal. What is the value of x?

x = 115 ( x \ 115)

Two parallel lines are crossed by a transversal. What is the value of x?

x = 70 (x \ 70)

What is the value of x? (35, 58)

x = 93

Which statement about the value of x is true?

x > 38

What is the value of x?

x=40

Two parallel lines are crossed by a transversal. What is the value of y?

y = 50

The given line segment has a midpoint at (−1, −2). What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

y = −4x − 6

What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )?

y = −6

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)?

y − 1 = −2(x − 4)

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)?

y − 5 = −(x − 2)

Lines c and d are parallel lines cut by transversal p. Which must be true by the corresponding angles theorem?

∠2 ≅ ∠6

In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS?

3 < QS < 13

In the diagram, line a is the perpendicular bisector of KM. What is the length of KM?

80 units

Triangle ABC is congruent to triangle XYZ. In ΔABC, AB = 12 cm and AC = 14 cm. In △XYZ, YZ = 10 cm and XZ = 14 cm. What is the perimeter of ΔABC?

36cm

Which set of side lengths represents a triangle with 3 lines of reflectional symmetry?

5,5,5

The value of x must be greater than (12, 15)

3

The rule ry = x • T4, 0(x, y) is applied to trapezoid ABCD to produce the final image A"B"C"D". Which ordered pairs name the coordinates of vertices of the pre-image, trapezoid ABCD? Check all that apply.

(-1, 0) (-1, -5) (1, -1) (1, -4)

Which point is on the line that passes through (0, 6) and is parallel to the given line?

(-12, 8)

Which diagram shows possible angle measures of a triangle?

B

4 2 2 6 Which description is true about the transformation shown?

It is a dilation because the transformation is not isometric.

In the diagram, which must be true for point P to be the centroid of the triangle?

JM = ML, LO = OK, and KN = NJ.

What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem?

L ≅ P

Trapezoid L'M'N'P' was constructed using trapezoid LMNP. For the transformation to be a translation, which statements must be true? Check all that apply.

LL'=PP' LL'=MM' Trapezoid LMNP is congruent to trapezoid L'M'N'P' All line segments that connect a point on the pre-image to its corresponding point on the image are parallel.

Janelle says that lines l and m are skew lines. Is Janelle correct?

No, because the lines are in the same plane.

ZE is the angle bisector of YEX and the perpendicular bisector of . is the angle bisector of YGZ and the perpendicular bisector of . is the angle bisector of ZFX and the perpendicular bisector of . Point A is the intersection of , , and . Which must be true?

Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.

ABC is an obtuse triangle. Which is true about point D?

Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located outside the triangle.

A transformation is shown in the diagram. Which transformation is shown?

Quadrilateral DEFG is reflected to form quadrilateral D'E'F'G'.

Triangle XYZ is rotated to create the image triangle X'Y'Z'. Which rules could describe the rotation? Check all that apply.

R0, 180° (x, y) → (-x, -y)

Quadrilateral ABCD is transformed according to the rule (x, y) → (y, -x). Which is another way to state the transformation?

R0, 270°

Triangle QRS is transformed as shown on the graph. Which rule describes the transformation?

R0, 270°

Square PQRS is transformed as shown on the graph. Which rule describes the transformation?

R0, 90°

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(-1, 2). The image of triangle XYZ after a rotation has vertices X'(-3, 1), Y'(0, 0), and Z'(-2, -1). Which rule describes the transformation?

R0, 90°

Which rule represents the translation from the pre-image, ABCD, to the image, A'B'C'D'?

T2, 1(x, y)

Consider the diagram. Which line segment has the same measure as TQ?

TR

A triangle has vertices at L(2, 2), M(4, 4), and N(1, 6). The traingle is transformed according to the rule R0, 180°. Which statements are true regarding the transformation? Check all that apply.

The rule for the transformation is (x, y) → (-x, -y). The coordinates of L' are (-2,-2). The coordinates of N' are (-1,-6)

Lines MN and PQ are parallel. Lines RS and TV intersect them. Which statements are true about these lines? Check all that apply.

The slope of line MN is . The slope of line RS is . Line RS is perpendicular to both line MN and line PQ.

Consider the triangle. Which statement is true about the lengths of the sides?

The three sides have the same length.

Which transformation maps the pre-image, DEFG, to the image, D'E'F'G'?

The transformation is a reflection.

A transformation of ΔDEF results in ΔD'E'F'. Which transformation maps the pre-image to the image?

The transformation is a rotation.

Triangle ABC is transformed to create triangle MNL. Which statement is true?

The transformation is rigid because corresponding side lengths and angles are congruent.

Triangle RST was transformed using the rule (x, y) → (-x, -y). The vertices of the triangles are R (1, 1) S (3, 1) T (1, 6) R' (-1, -1) S' (-3, -1) T' (-1, -6) Which best describes the transformation?

The transformation was a 180° rotation about the origin.

Triangle ABC was transformed using the rule (x, y) → (-y, x). The vertices of the triangles are shown. A (-1, 1) B (1, 1) C (1, 4) A' (-1, -1) B' (-1, 1) C' (-4, 1) Which best describes the transformation?

The transformation was a 90° rotation about the origin.

Order of Symmetry List:

http://bestmaths.net/online/index.php/year-levels/year-10/year-10-topics/symmetry/

Two parallel lines are crossed by a transversal. What is the value of k?

k = 60

Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)?

line HJ

How can ΔWXY be mapped to ΔMNQ? First, translate vertex W to vertex M. Next, reflect ΔWXY across the line containing____

line segment WX

Planes Q and R are parallel planes. Plane Q contains line a. Plane R contains line b. If a third plane could be drawn which contains both lines a and b, then

lines a and b must be parallel.

Complete the statement. Since angle B is the largest angle,________ is the side

longest

Gene starts from home and travels 3 miles north to the shopping mall. From the shopping mall, he travels 2 miles west to the library. Then, from the library, he travels about 3.6 miles to return home. The entire trip forms a triangle. The largest angle made during his trip is at

the mall

In the diagram, Z is the circumcenter of triangle TUV. What is the length of VZ?

10 units

In triangle NLM, point S is the centroid, QS = (3x - 5) cm, and NS = (4x) cm. What is NS?

20 cm

Point Y is the circumcenter of ΔDEF. Find the length of FY. FY measures ____ units

22

Quadrilateral ABCD is reflected over line y as shown, resulting in quadrilateral TURS. If AD 5 in., AB = 7 in., DC = 4 in., and BC = 9 in., what is TU?

7 in.

Point P is the incenter of ΔRST. Which must be true?

BP=PC

Point Y is the circumcenter of triangle DEF. Which statement is true about point Y?

Point Y is the center of the circle that passes through points D, E, and F.

Which explains whether ΔFGH is congruent to ΔFJH?

They are not congruent because only one pair of corresponding sides is congruent.

How can a translation and a rotation be used to map ΔHJK to ΔLMN?

Translate K to N and rotate about K until HK lies on the line containing LN.

Which shows two triangles that are congruent by the SSS congruence theorem?

XX a

The isosceles triangle has a base that measures 14 units. The value of y, the length of each leg, must be

greater than 7

Which is a true statement about the diagram?

m∠1 + m∠2 = 180°

The proof that ΔACB ≅ ΔECD is shown. Given: AE and DB bisect each other at C. Prove: ΔACB ≅ ΔECD What is the missing statement in the proof?

∠ACB ≅ ∠ECD

What is the smallest angle of rotational symmetry for a square?

90

A centroid is the intersection of three

medians in a triangle.

Two parallel lines are crossed by a transversal. What is the value of x?

x = 12 (5x+5 \ 115)

Two parallel lines are crossed by a transversal. What is the value of x?

x = 37 (3x+4 \ 115)

The value of x is (9x, 5x, 9+x)

3

What value of n would make point A the circumcenter?

3

The figure was created by repeatedly reflecting triangle NMP. What is the perimeter of the figure?

42

Which statements are always true regarding the diagram? Check all that apply.

m∠5 + m∠3 = m∠1 m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

If bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Check all that apply.

m∠ABC = 125° and AB ≅ DB CD = 52 cm AB = 29 cm

In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

m∠X + m∠Y < 90°

The triangles are congruent by SSS. Which transformation(s) can be used to map one triangle onto the other?

reflection only rotation, then translation

Which of these triangle pairs can be mapped to each other using both a translation and a rotation about C?

D

Which shows two triangles that are congruent by ASA?

B

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments_______ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SA

MS and QS

Triangles RQS and NTV have the following characteristics: • Right angles at ∠Q and ∠T • RQ ≅ NT Can it be concluded that ΔRQS ≅ ΔNTV by SAS? Why or why not?

No, it is necessary to know that another set of corresponding sides is congruent.

In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK?

Point G cannot be a centroid because JG is shorter than GE.

Triangle XYZ is shown, where n ≥ 5. Which statements are true regarding the sides and angles of the triangle? Check all that apply.

XX a,c,e

Iliana claims that she can construct a triangle from a 12-inch rod, a 36-inch rod, and a 39.4-inch rod. Which statement explains whether she is correct?

XX try c Iliana will be able to construct a triangle because the sum of any two sides is less than the third side.

Which rigid transformation would map ΔAQR to ΔAKP?

a rotation about point A

Two rigid transformations are used to map ΔHJK to ΔLMN. The first is a translation of vertex H to vertex L. What is the second transformation?

a rotation about point H

Two rigid transformations are used to map JKL to MNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?

a rotation about point L

The triangles are congruent by the SSS congruence theorem. Which rigid transformation(s) can map ABC onto FED?

reflection, then translation

The triangles are congruent by SSS or HL. Which transformation(s) can map MNQ onto PQN?

rotation, then translation

Which is the only center point that lies on the edge of a triangle?

the circumcenter of a right triangle

Fiona's school has three hallways that make up three sides of a triangular building design. In the morning, Fiona walks 90 yards through the first hallway to get to the next. In the afternoon, she walks 60 yards through a second hallway to exit the building. What are the possible lengths of the third hallway that she did not walk through?

between 30 yards and 150 yards

The proof that ΔEFG ≅ ΔJHG is shown. Given: G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ. Prove: ΔEFG ≅ ΔJHG What is the missing statement in the proof?

∠GFE ≅ ∠GHJ

Triangle QRS has the angle measures shown. m∠Q = (1x)° m∠R = (3x)° m∠S = (6x)° The measure of the obtuse angle equals

108

In triangle ABC, EG = x inches and BG = (5x - 12) inches. What is EB

12

In the diagram, GB = 2x + 3.. What is GB?

15

In triangle DEF, CG = (x + 5) units and DG = (3x - 2). What is DG?

34

For the triangles to be congruent by HL, what must be the value of x?

4

Which are the possible side lengths of a triangle?

4 cm, 8 cm, 10 cm

Point O is the incenter of triangle ABC. What is mQOB?

75

Consider the triangle. Which shows the order of the angles from smallest to largest?

angle B, angle A, angle C

Quadrilateral ABCD is rotated 145° about point T. The result is quadrilateral A'B'C'D'. Which congruency statement is correct?

ABCD ≅ A'B'C'D'

In the triangles, QR = DE and SR = FE. Which statement about the sides is true?

DF < QS

Based on the given angle measures, which triangle has side length measures that could be correct?

D

Which additional information, if true, would help to prove that ΔLMP ≅ ΔNMP by HL? Check all that apply.

Line MK is the perpendicular bisector of LN. ML ≅ MN

Triangle GHJ is rotated 90° about point X, resulting in triangle STR. Which congruency statement is true?

TS ≅ HG

Which statements are true about additional information for proving that the triangles are congruent? Check all that apply.

XX If A ≅ T, then the triangles would be congruent by ASA. If B ≅ P, then the triangles would be congruent by AAS. If C and Q are right angles, then triangles would be congruent.

The triangles shown are congruent by the SSS congruence theorem. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B"C". What is the sequence of the transformations?

XX rotation, then reflection, then translation

In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?

XX ∠J ≅ ∠M

Triangle XYZ was translated up 2 and right 3 units, creating triangle CAB. Which relationship between the parts of the two triangles must be true?

YZ ≅ AB

Can a translation and a reflection map QRS to TUV? Explain why or why not.

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.

Point A is the point of concurrency of the angle bisectors of ΔDEF. What is the length of ZA?

ZA = 3cm

Which rigid transformation would map MZK to QZK?

a reflection across the line containing ZK