Answers EBR - Geometry A-CR SUMMER 2026Unit Test

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The proof that MNG ≅ KJG is shown.Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG

the reflexive property

ASA

AAS

the third angle theorem

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Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20.

9 units

12 units

15 units

18 units

Triangle RST was dilated by a scale factor of . The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units.

4 units

8 units

16 units

20 units

is an altitude in triangle WXZ.

XWZ is an obtuse angle.

XWZ is a right angle.

XWZ is congruent to WXY.

XWZ is congruent to XZW.

Triangles J K L and M N R are shown.

KL ≅ NR

∠L ≅ ∠R

∠K ≅ ∠N

JK ≅ MN

Quadrilateral JKLM was dilated according to the ruleDO,(x,y) to create the image quadrilateral J'K'L'M', which is shown on the graph.

(0, -4)

(0, -1)

(0, 0)

(0, 4)

Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Yes, they are congruent by either ASA or AAS.

Yes, they are both right triangles.

No, M is not congruent to NLQ.

No, there are no congruent sides.

The proof that ΔQPT ≅ ΔQRT is shown.Given: SP ≅ SRProve: ΔQPT ≅ ΔQRT

definition of perpendicular bisector

definition of congruence

reflexive property

substitution property

Triangles D E F and G H J are congruent. Triangle D E F is shifted down and to the right to form triangle G H J.

dilation

reflection

rotation

translation

Question text not available

3 ft

4 ft

18 ft

12 ft

Triangle ABC was dilated using the rule .

10 units

12 units

16 units

20 units

Parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.

One-eighth

One-fourth

Read the proof.Given: AB ∥ DEProve: △ACB ~ △DCE

AA similarity theorem.

SSS similarity theorem.

AAS similarity theorem.

ASA similarity theorem.

Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3.

Which best explains why all equilateral triangles are similar?

All equilateral triangles can be mapped onto each other using dilations.

All equilateral triangles can be mapped onto each other using rigid transformations.

All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.

All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.

∠DFE is 4 times greater than ∠GFH.

∠FHG is the measure of ∠FED.

∠DFE is congruent to ∠GFH.

∠FHG is congruent to ∠EFD.

Consider △RST and △RYX.

StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction

StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction

StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction

StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction

Which pair of triangles can be proven congruent by SAS?

2 identical triangles are shown. The triangle is reflected across a line to form the second triangle.

2 identical triangles are shown. The triangle is rotated 90 degrees to form the second triangle.

2 identical triangles are shown. The triangle is reflected across a line and then rotated to form the second triangle.

2 identical triangles are shown. The triangle is rotated up and to the left 90 degrees to form the second triangle.

If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?

0.1

Option

Triangles A B C and Q R S are shown. Sides A B and Q R are congruent. Angles C A B and R Q S are congruent. Angles Q S R and A C B are congruent.

a reflection across the line containing AB

a rotation about point B

a reflection across the line containing CB

a rotation about point C

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

LO ≅ LM

OA ≅ MA

LOA ≅ LMA

LAO ≅ LAM

Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2 and the length of P B is 3. The Length of A A prime is 4 and the length of B B prime is 5.

Yes, it is an enlargement with a scale factor of 3.

Yes, it is an enlargement with a scale factor of .

No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.

No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.

Consider the two triangles.

Option

Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

Yes, if JL ≅ XZ.

Yes, if XZ = 10.

No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

No, because the leg of one triangle is equal in length to the leg of the other triangle.

Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.

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