Geometry A

Which points lie on the line that passes through point P and is parallel to the given line? Select three options. (-4, 2) (-1, 3) (-2, 2) (4, 2) (-5, -1)

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

Quadrilateral FGHJ is dilated according to the rule DO,2/3 (x,y)-> (2/3x,2/3y) to create the image quadrilateral F'G'H'J', which is not shown. What are the coordinates of point J'? (-2,-4) (-2,-6) (-9/2, -4) (-9/2,-9)

(-2,-4)

Which point is on the line that passes through point R and is perpendicular to line PQ? (-6, 10) (-4, -8) (0, -1) (2, 4)

(-4, -8)

Triangle ABC will be dilated according to the rule D F,0.25(x,y), where point F is the center of dilation. What will be the coordinates of vertex A' of the image? (-8,-4) (-2,-1) (0, 0) (1, 0)

(1,0)

In the diagram, DC is 10 units and BC is 6 units. What is the length of segment AC? 6 units 8 units 12 units 16 units

12 units

https://media.edgenuity.com/evresources/8101/8101-01/8101-01-05/8101-01-05-assessment/8101-01-05-21.png What is mPHJ? 100° 120° 140° 160°

120

Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X? 45° 60° 120° 135°

135

In the diagram, the length of segment TR can be represented by 5x - 4. What is the length of segment VS? 3 units 11 units 13 units 15 units

15 units

Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym the distance from Ping's home to Ari's home. Where is the gym? 9th Street and 10th Avenue 12th Street and 12th Avenue 14th Street and 12th Avenue 15th Street and 14th Avenue

15th Street and 14th Avenue

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 24 mm 32 mm 48 mm

16mm

What must be the value of x so that lines c and d are parallel lines cut by transversal p? 12 18 81 99

18

Points Q and R are midpoints of the sides of triangle ABC. What is AQ? 10 units 14 units 20 units 32 units

20 units

In the diagram, mFLI is 106°, mFLG = (2x - 1)°,mGLH = (x + 17)°, and mHLI = (4x - 15)°. What is the measure of the smallest angle in the diagram? 15° 29° 32° 45°

29

What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio? -1 0 2 3

3

In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS? QS = 13 5 < QS < 8 QS > 13 3 < QS < 13

3 < QS < 13

Triangle ABC is rotated 45° about point X, resulting in triangle EFD. If EF = 4.2 cm, DF = 3.6 cm, and DE = 4.5 cm, what is CB? 3.3 cm 3.6 cm 4.2 cm 4.5 cm

3.6 cm

Angles 1 and 2 are complementary and congruent. What is the measure of angle 1? 30° 45° 50° 75°

45

What is the length of ? 58 cm 75 cm 88 cm 116 cm

58 cm

Triangle DEF is isosceles, where . Angle FDE is bisected by segment DG, creating angle GDE with a measure of 29°. What is the measure of angle DFE? 29° 32° 58° 64°

58°

What is the x-coordinate of the point that divides the directed line segment from K to J into a ratio of 1:3? K (9,2) J (1,-10) -1 3 7 11

7

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle? 27° 36° 54° 72°

72

What value is a counterexample for the conditional statement shown? If a number between 0 and 100 is an odd perfect square, then the only factors of the number are 1, the number itself, and the square root of the number. 9 25 49 81

81

Which value of x would make FG||BC? 1 3 6 9

9

Which best describes the dimensions of a plane? A plane has zero dimensions because it represents a location on the coordinate plane. A plane has one dimension because it is made up of an infinite number of points. A plane has two dimensions because it is a flat surface that has length and width but no depth. A plane has three dimensions because it is made up of exactly three noncollinear points.

A plane has two dimensions because it is a flat surface that has length and width but no depth.

Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto's proof that was not included in Nessa's proof? Given: B ≅ N; BC ≅ NM; C is right; M is rightProve: ABC ≅ QNM A ≅ Q because of the third angle theorem. AB ≅ QN because they are both opposite a right angle. BC ≅ NM because it is given. C ≅ M because right angles are congruent.

A ≅ Q because of the third angle theorem.

Which composition of transformations maps figure RSTUV to figure R"S"T"U"V"? a reflection across line n followed by a translation down and to the right a reflection across line n followed by a 270° rotation about point P a translation down followed by a 270° rotation about point P a translation down followed by a reflection across line n

B. a reflection across line n followed by a 270° rotation about point P

The statements below can be used to prove that the triangles are similar. ? △ABC ~ △XYZ by the SSS similarity theorem. Which mathematical statement is missing? YZ/BC = 6/3 ∠B ≅ ∠Y BC/YZ = 6/3 ∠B ≅ ∠Z

BC/YZ = 6/3

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

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

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

Figure A

Consider the diagram. The congruence theorem that can be used to prove △BAE ≅ △CAD is SSS. ASA. SAS. HL.

HL

Which congruence theorem can be used to prove △BDA ≅ △DBC? HL SAS AAS SSS

HL

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options. HL SAS SSS ASA AAS

HL, SAS, SSS

The converse of a conditional statement is "If the sum of the exterior angles of a figure is 360°, then the figure is a polygon." What is the inverse of the original conditional statement? If a figure is a polygon, then the sum of the exterior angles is 360°. If the sum of the exterior angles of a figure is not 360°, then the figure is not a polygon. If the sum of the exterior angles of a figure is 360°, then the figure is not a polygon. If a figure is not a polygon, then the sum of the exterior angles is not 360°.

If a figure is not a polygon, then the sum of the exterior angles is not 360°.

Which statement can be concluded using the true statements? If a quadrilateral has 4 equal sides and 4 equal angles, then it is a square.If a figure is a square, then each of its angles must measure 90 degrees. If a quadrilateral has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees. If a quadrilateral has 4 equal sides and 4 equal angles, then none of its angles measures 90 degrees. If all four angles in a quadriateral measure 90 degrees, the quadrilateral is a square. If all four angles in a quadriateral measure 90 degrees, the quadrilateral cannot be a square.

If a quadrilateral has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.

Which angles form a linear pair? PRL and LRM ORP and MRN MRN and NRO LRP and ORP

MRN and NRO

Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio. Are P and Q the same point? Why or why not? Yes, they both partition the segment into a 1:3 ratio. Yes, they are both 1/4 the distance from one endpoint to the other. No, P is 1/4 the distance from A to B, and Q is 1/4 the distance from B to A. No, Q is closer to A and P is closer to B

No, P is 1/4 the distance from A to B, and Q is 1/4 the distance from B to A.

Which point is located on ray PQ? point M point N point O point R

Point R

Triangle PQR was dilated according to the rule DO,2(x,y)(2x,2y) to create similar triangle P'Q'Q. Which statements are true? Select two options. ∠R corresponds to ∠P'QQ'. ∠PQR corresponds to ∠QPQ'. Segment QQ' is parallel to segment PP'. Side RQ corresponds to side QQ'. △PQR ≅ △P'Q'Q

R corresponds to ∠P'QQ'.Side RQ corresponds to side QQ'.

Triangle QRS is transformed as shown on the graph. Which rule describes the transformation? R0, 90° R0, 180° R0, 270° R0, 360°

R0, 270°

Triangle XYZ with vertices X(0, 0), Y(0, -2), and Z(-2, -2) is rotated to create the image triangle X'(0, 0),Y'(2, 0), and Z'(2, -2). Which rules could describe the rotation? Select two options. R0, 90° R0, 180° R0, 270° (x, y) → (-y, x) (x, y) → (y, -x)

R0, 90°,(x, y) → (-y, x)

Which shows the sides in order from longest to shortest? PQ RQ RP RQ PQ RP RQ RP PQ RP PQ RQ

RQ PQ RP

In the diagram, which angles form a linear pair? Select three options. RST and RSV RST and TSU RST and VSU TSU and USV TSU and RSV

RST and RSV RST and TSU TSU and USV

Which statement must be true about the diagram? Point K is a midpoint of JL mJKN = 1/2 mJKM Ray KM is an angle bisector of NKL. JK = 1/2 KL

Ray KM is an angle bisector of NKL.

Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"? T-6,-2 r x-axis(x,y) r x-axis T -6,-2(x,y) T-6,-2 R0,90(x,y) R0,90 T-6,-2(x,y)

T-6,-2 r x-axis(x,y)

A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation? T1, -9(x, y) T-1, -9(x, y) T-9, 1(x, y) T-9, -1(x, y)

T1, -9(x, y)

Which best explains whether or not triangles RST and ACB are congruent? The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left. The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the y-axis and a translation 2 units down. The figures are not congruent. Point R corresponds to point A, but S corresponds to B and T corresponds to C. The figures are not congruent. Point R does not correspond with point A.

The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left.

Planes S and R both intersect plane T . Which statements are true based on the diagram? Select three options. Plane S contains points B and E. The line containing points A and B lies entirely in plane T. Line v intersects lines x and y at the same point. Line z intersects plane S at point C. Planes R and T intersect at line y.

The line containing points A and B lies entirely in plane T. Line z intersects plane S at point C. Planes R and T intersect at line y.

Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.

They are parallel because their slopes are equal.

Why are lines AC and RS skew lines? They lie in different planes and will never intersect. They lie in the same plane but will never intersect. They lie in different planes but will intersect if a plane is drawn to contain both lines. They lie in different planes and will be parallel if a plane is drawn to contain both lines.

They lie in different planes and will never intersect.

Is ΔWXZ ≅ ΔYZX? Why or why not? Yes, they are congruent by SAS. Yes, they are both right triangles. No, the triangles share side XZ. No, there is only one set of congruent sides.

Yes, they are congruent by SAS.

Which two undefined geometric terms always describe figures with no beginning or end? a line and a plane a line and a point a distance and a plane a distance and a point

a line and a plane

Which defines a line segment? two rays with a common endpoint a piece of a line with two endpoints a piece of a line with one endpoint all points equidistant from a given point

a piece of a line with two endpoints

Which rigid transformation would map ΔABC to ΔABF? a rotation about point A a reflection across the line containing CB a reflection across the line containing BA a rotation about point B

a reflection across the line containing BA

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

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

Which new angle is created by extending one side of a triangle? a remote interior angle an adjacent interior angle an exterior angle a complementary angle

an exterior angle

Which pair of triangles can be proven congruent by the HL theorem?

c

Given the information in the diagram, which theorem best justifies why lines e and f must be parallel? alternate interior angles theorem same side interior angles theorem converse of the alternate interior angles theorem converse of the same side interior angles theorem

converse of the same side interior angles theorem

Which diagram shows lines that must be parallel lines cut by a transversal? 91, 91 91, 91 89,91 91,89

d. 91, 89

(3h+18) (15h) What is the value of h? h = 1.5 h = 9 h = 10 h = 13.5

h=9

Consider the two planes. In the diagram, the only figure that could be parallel to line c is line a. line b. line d. plane Q.

line d

Two parallel lines are crossed by a transversal. What is the value of m? m = 68 m = 78 m = 102 m = 112

m = 102

Angles 1 and 2 are supplementary. Which equation represents the relationship between their measures? m1 + m2 = 90° m1 + m2 = 100° m1 + m2 = 180° m1 + m2 = 200°

m1 + m2 = 180°

What is the measure of 15? m15 = 77° m15 = 83° m15 = 93° m15 = 97°

m15 = 97°

Consider the triangle. 12 15 8 The measures of the angles of the triangle are 32°, 53°, 95°. Based on the side lengths, what are the measures of each angle? mA = 95°, mB = 53°, mC = 32° mA = 32°, mB = 53°, mC = 95° mA = 43°, mB = 32°, mC = 95° mA = 53°, mB = 95°, mC = 32°

mA = 32°, mB = 53°, mC = 95°

Triangle ABC has the angle measures shown. mA=(2x) mB=(5x) mC=(11x) Which statement is true about the angles? mA=20 mB=60 A and B are complementary mA+mC=120

mA=20

In the triangles, and . If RT is greater than BA, which correctly compares angles C and S? mC = mS mC < mS mC > mS mC ≥ mS

mC < mS

In the triangles, HG = MP and GK = PN. Which statement about the sides and angles is true? mG > mP mP > mG HK = MN HG = PN

mG > mP

67, 60 What is m∠ABC? m∠ABC = 60° m∠ABC = 67° m∠ABC = 120° m∠ABC = 127°

m∠ABC = 127°

Triangle DEF is congruent to D'EF' by the SSS theorem. Which single rigid transformation is required to map DEF onto D'EF'? dilation reflection rotation translation

rotation

What is the rule for the reflection? rx-axis(x, y) → (-x, y) ry-axis(x, y) → (-x, y) rx-axis(x, y) → (x, -y) ry-axis(x, y) → (x, -y)

ry-axis(x, y) → (-x, y)

Which is logically equivalent to the converse of a conditional statement? the original conditional statement the inverse of the original conditional statement the contrapositive of the original conditional statement the converse of the converse statement

the inverse of the original conditional statement

How can ΔABC be mapped to ΔXYZ? First, translate ____________________. Next, rotate ΔABC about B to align the sides and angles. vertex B to vertex Z vertex B to vertex Y vertex A to vertex Z vertex A to vertex Y

vertex B to vertex Y

Given: and g is a transversal Prove: 1 and 8 Given that and g is a transversal, we know that by the alternate interior angles theorem. We also know that and by the ________. Therefore, by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

vertical angles theorem

What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8

x + 2y = 8

A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft. Which expression represents the possible values of n, in feet? Express your answer in simplest terms. x - 1 < n < 3x + 5 n = 3x + 5 n = x - 1 3x + 5 < n < x - 1

x - 1 < n < 3x + 5

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)? y = -1/3x + 5 y = -1/3x + 3 y = 3x + 2 y = 3x − 5

y = 3x − 5

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) y - 1 = -1/2(x - 4) y - 1 = 1/2(x - 4) y − 1 = 2(x − 4)

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 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)

y − 5 = −(x − 2)

Triangle RST is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures? ΔRST ≅ ΔACB ΔRST ≅ ΔABC ΔRST ≅ ΔBCA ΔRST ≅ ΔBAC

ΔRST ≅ ΔBAC

△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX.1. given2. AB ≅ AC and AY ≅ AX2. definition of isosceles triangle3. AB = AC and AY = AX3. definition of congruency4. AY • AC = AX • AC4. multiplication property of equality5. AY • AC = AX • AB5. substitution property of equality6. 6. division property of equality7. 7. division property of equality8. ?8. ?9. △ABC ~ △AYX9. SAS similarity theorem Which statement and reason are missing in the proof? ∠A ≅ ∠A; reflexive property ∠X ≅ ∠X; reflexive property ∠ABC ≅ ∠AYX; corresponding angles of similar triangles ∠ABC ≅ ∠AXY; corresponding angles of similar triangles

∠A ≅ ∠A; reflexive property

△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. The proof that △ABC ~ △AYX is shown. StatementsReasons1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX.1. given2. AB ≅ AC and AY ≅ AX2. definition of isosceles triangle3. AB = AC and AY = AX3. definition of congruency4. AY • AC = AX • AC4. multiplication property of equality5. AY • AC = AX • AB5. substitution property of equality6. 6. division property of equality7. 7. division property of equality8. ?8. ?9. △ABC ~ △AYX9. SAS similarity theorem Which statement and reason are missing in the proof? ∠A ≅ ∠A; reflexive property ∠X ≅ ∠X; reflexive property ∠ABC ≅ ∠AYX; corresponding angles of similar triangles ∠ABC ≅ ∠AXY; corresponding angles of similar triangles

∠A ≅ ∠A; reflexive property

To prove that ΔAED ˜ ΔACB by SAS, Jose shows that . Jose also has to state that ∠A≅ ∠A ∠A ≅ ∠D ∠A ≅ ∠ACB ∠A ≅ ∠ABC

∠A≅ ∠A

Which pair of angles is supplementary? ∠RXZ and ∠YXZ ∠PXQ and ∠RXS ∠YZX and ∠UZT ∠WZX and ∠XYZ

∠RXZ and ∠YXZ

In the diagram, . To prove that △VWZ ~ △YXZ by the SAS similarity theorem, which other sides or angles should be used? WV and XY WV and ZY ∠VZW ≅ ∠YZX ∠VWZ ≅ ∠YXZ

∠VZW ≅ ∠YZX

Line RS intersects triangle BCD at two points and is parallel to segment DC. Which statements are correct? Select three options. △BCD is similar to △BSR. BR/RD=BS/SC If the ratio of BR to BD is , then it is possible that BS = 6 and BC = 3. (BR)(SC) = (RD)(BS) BR/RS=BS/SC

△BCD is similar to △BSR, BR/RD=BS/SC, (BR)(SC) = (RD)(BS)

The proof that UX ≅ SV is shown. Given: △STU an equilateral triangle ∠TXU ≅ ∠TVS Prove: UX ≅ SV What is the missing statement in the proof? StatementReason1. ∠TXU ≅ ∠TVS1. given2. ∠STV ≅ ∠UTX2. reflex. prop.3. △STU is an equilateral triangle3. given4. ST ≅ UT4. sides of an equilat. △ are ≅5. ?5. AAS6. UX ≅ SV6. CPCTC △SXU ≅ △TVS △UVX ≅ △SXV △SWX ≅ △UWV △TUX ≅ △TSV

△TUX ≅ △TSV