Answers EBR - Geometry A-CR SUMMER 2026Unit Test

Unit Test — Cumulative exam Answers

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Given: HF || JK; HG ≅ JGProve: FHG ≅ KJG

FGH ≅ KGJ because vertical angles are congruent.

JKG ≅ HFG because vertical angles are congruent.

FHG ≅ JKG because right angles are congruent.

HFG ≅ KJG because alternate interior angles are congruent.

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On a coordinate plane, a triangle has points R (negative 3, 4), T (negative 1, negative 4), and S (negative 4, negative 2).

(–4, 3)

(4, –3)

(–3, –4)

(3, 4)

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.

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

Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.

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

Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent.

Yes, but only if AB ≅ DC.

Yes, but only if BC ≅ DC.

No, because AB is not congruent to AC.

No, because AB ≅ DA.

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ,2.25.

x = 2.25 units

x = 2.5 units

x = 4.25 units

x = 4.5 units

To prove that ΔAED ˜ ΔACB by SAS, Jose shows that .

Option

Lines e and f are intersected by line a. At the intersection of lines a and e, the bottom right angle is 72 degrees. At the intersection of lines a and f, the uppercase right angle is 108 degrees.

alternate interior angles theorem

same side interior angles theorem

converse of the alternate interior angles theorem

converse of the same side interior angles theorem

On a coordinate plane, a line goes through (1, negative 1) and (4, 2). A point is at (2, 5).

y + 5 = x + 2

y − 2 = x − 5

y − 5 = −(x − 2)

y + 2 = −(x + 5)

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

2 right triangles have congruent hypotenuses.

2 triangles have one congruent angle and 2 congruent sides.

2 right triangles have congruent hypotenuses and another congruent side.

2 triangles have 3 congruent sides.

Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Select two options.

The rule for the translation can be written as T–3, 1(x, y).

The rule for the translation can be written as T–1, 3(x, y).

The rule for the translation can be written as(x, y) → (x + 1, y – 3).

The rule for the translation can be written as(x, y) → (x – 3, y + 1).

Trapezoid ABCD has been translated 3 units to the right and 1 unit up.

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).

T4, –4(x, y)

T–4, –4(x, y)

T2, –4(x, y)

T–2, –4(x, y)

Triangles D E F and D prime E prime F prime are connected at point E. Triangle D E F is rotated about point E to form triangle D prime E prime F prime.

dilation

reflection

rotation

translation

Which pair of triangles can be proven congruent by SAS?

2 triangles with identical angle measures are shown. The second triangle is shifted to the right.

2 triangles are shown. They have 2 congruent sides and a congruent angle. The first triangle is rotated about a point to form the second triangle.

2 triangles are shown. They have 1 congruent side and 2 congruent angles. The first triangle is rotated about a shared side to form the second triangle.

Option

Rectangle ABCD was dilated to create rectangle A'B'C'D' using point R as the center of dilation.

3 units

5 units

6 units

9 units

Which graph shows a dilation?

On a coordinate plane, 2 triangles are shown. The smaller triangle has points (negative 2, 0), (negative 2, 1), and (0, 0). The larger triangle has points (negative 3, 0), (negative 3, 4), and (2, 0).

On a coordinate plane, 2 triangles are shown. The smaller triangle has points (negative 2, 0), (negative 2, 2), and (1, 0). The larger triangle has points (negative 3, 0), (negative 3, 4), and (2, 0).

On a coordinate plane, 2 triangles are shown. The smaller triangle has points (negative 1, 0), (negative 1, 1), and (2, 0). The larger triangle has points (negative 2, 0), (negative 2, 3), and (4, 0).

On a coordinate plane, 2 triangles are shown. The smaller triangle has points (negative 1, 0), (negative 1, 2), and (3, 0). The larger triangle has points (negative 2, 0), (negative 2, 3), and (4, 0).

Triangle ABC will be dilated according to the rule(x,y), where point F is the center of dilation.

(-8,-4)

(-2,-1)

(0, 0)

(1, 0)

Which part of the proof does the fourth statement and reason represent?Given: AB ≅ BCBC ≅ EF Prove: EG = AB + FG

It is part of the given information.

It is part of the argument.

It is the conclusion.

It is an assumption.

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

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.

Four lines extend from point K. The space between lines K J and K N is 58 degrees. The space between lines K N and K M is 61 degrees. The space between lines K M and K L is 61 degrees.