Geometry Cumulative Exam Review

What is the scale factor of the dilation of triangle DEF?

3/10

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

32.8°

Which best explains whether or not ΔABC ≅ ΔLMN?

The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

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

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

3 < QS < 13

Which statement describes the order of rotational symmetry for an isosceles triangle?

An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.

Which pair of triangles can be proven congruent by SAS?

B

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

HL.

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.

Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth.

JKM is not a right triangle because KM ≠ 15.3.

How can ΔABC be mapped to ΔXYZ? First, translate ___________________. Next, rotate ΔABC about B to align the sides and angles.

vertex B to vertex Y

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

x + 2y = 8

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

(-2,-4)

What are the coordinates of the midpoint of AB?

(-3/2,-1)

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

(-4, -8)

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

(3, 4)

The midpoint of is point P at (−16,6). If point A is at (−10,8), what are the coordinates of point B?

(−22,4)

To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?

-2/5

The table represents a linear function. What is the slope of the function?

-4

A regular decagon has 10 sides. How many reflectional symmetries does a regular decagon have?

10

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?

29°

What is the length of MN ?

58 cm

Angle MON is a straight angle and bisects MOQ. What is the measure of MOP?

61°

Which value of x would make FG||BC?

9

Which diagram shows possible angle measures of a triangle?

B

Which congruence theorem can be used to prove △BDA ≅ △DBC?

HL

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

The diagram shows several points and lines. Which statements are true based on the diagram? Check all that apply.

There is only one line that can be drawn through points L and P. Points J, K, and Q are collinear.

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

They are not parallel because their slopes are not equal.

Could ΔABC be congruent to ΔADC by SSS? Explain.

Yes, but only if BC ≅ DC.

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 about the point P

Which two undefined geometric terms always describe figures with no beginning or end?

a line and a plane

Which defines a line segment?

a piece of a line with two endpoints

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

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

an exterior angle

Given: g ∥ h and ∠2 ≅ ∠3 Prove: e ∥ f Statements Reasons 1. g || h 1. given 2. ∠1 ≅ ∠2 2. corresponding angles theorm 3. ∠2 ≅ ∠3 3. given 4. ∠1 ≅ ∠3 4. transitive property 5. e || f 5. ? What is the missing reason in the proof?

converse alternate interior angles theorem

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

converse of the same side interior angles theorem

In the triangles, and . If RT is greater than BA, which correctly compares angles C and S?

mC < mS

Triangle ABC has the angle measures shown. Which statement is true about the angles?

m∠A=20°

Let p: The integer has one digit. Let q: The integer is less than Which represents "The integer has one digit if and only if the integer is less than 10"?

p ↔ q

Which point is located on ray PQ?

point R

The truth table represents statements p, q, and r. p q r A T T T B T T F C T F T D T F F E F T T F F T F G F F T H F F F Which statement is true for rows A, C, and E?

r → (p ∨ q)

Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP Statement Reason 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given 2. m∠H + m∠J + m∠K = 180° 2. ? 3. 30° + 50° + m∠K = 180° 3. substitution property 4. 80° + m∠K = 180° 4. addition 5. m∠K = 100° 5. subtraction property of equality 6. m∠J = m∠P; m∠K = m∠N 6. substitution 7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent 8. △HKJ ~ △LNP 8. AA similarity theorem Which reason is missing in step 2?

triangle angle sum theorem

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? Check all that apply.

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

Which pair of angles is supplementary?

∠RXZ and ∠YXZ

Line RS intersects triangle BCD at two points and is parallel to segment DC. Which statements are correct? Check all that apply.

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

Let p: The day is Tuesday. Let q: The day is Thursday. Let r: She comes to work. Which represents the statement "The day is Tuesday or Thursday if and only if she comes to work"?

(p ∨ q) ↔ r

The midpoint of FG is point H at (-5, 2). One endpoint is G(-9, -6). What is the y-coordinate of the other endpoint? The y-coordinate of the other endpoint is ________.

10

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?

15th Street and 14th Avenue

Use the ruler to measure the length of to the nearest centimeter. The length of is _________ centimeters.

18

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

3

To prove that △AED ~ △ACB by SAS, Jose shows that . Jose also has to state that ∠A is congruent to ∠________.

A

Which best describes the dimensions of a plane?

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 right Prove: ABC ≅ QNM

A ≅ Q because of the third angle theorem.

Which best explains whether or not all isosceles triangles are similar?

All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

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?

BC/YZ=6/3

Point Z is equidistant from the vertices of ΔTUV. Which must be true?

BTZ BUZ

Given: HF || JK; HG ≅ JG Prove: FHG ≅ KJG To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

FGH ≅ KGJ because vertical angles are congruent.

Consider the two planes. In the diagram, the only figure that could be parallel to line c is ________.

Line D

In triangle ABC, the segments drawn from the vertices intersect at point G. Segment FG measures 6 cm, and segment FC measures 18 cm.

Point G can be the centroid because 12:6 equals 2:1.

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°

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

T-6, -2°rx-axis(x,y)

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

T-6,-2°rx-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)

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)

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

They lie in different planes and will never intersect.

What are the rigid transformations that will map △ABC to △DEF?

Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.

Which transformations could have taken place to map △ABC to △A"B"C"?

a translation and a dilation

What is the format of this proof? Given: ∠ABC is a right angle, ∠DBC is a straight angle Prove: ∠ABD is a right angle

two-column proof

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

Point A is at -2 and point B is at 5. Which shows how to determine the point that will divide the segment into a 4:5 ratio using the formula x = (x2 - x1) + x1?

x = (4/9) (5 + 2) - 2

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ,2.25. What is x, the distance between points S' and S?

x = 2.5 units

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

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)

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)

Triangle RST is rotated 180° about the origin, and then translated up 3 units. Which congruency statement describes the figures?

ΔRST ≅ ΔBAC