Answers EBR - Geometry A-CR SUMMER 2026Right Triangle Similarity

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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.

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△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX.

∠A ≅ ∠A; reflexive property

∠X ≅ ∠X; reflexive property

∠ABC ≅ ∠AYX; corresponding angles of similar triangles

∠ABC ≅ ∠AXY; corresponding angles of similar triangles

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

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle.

ΔJKM

ΔMKL

ΔKML

ΔLJK

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?

StartFraction Y Z Over B C = StartFraction 6 Over 3 EndFraction

∠B ≅ ∠Y

StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction

∠B ≅ ∠Z

In the diagram, .

WV and XY

WV and ZY

∠VZW ≅ ∠YZX

∠VWZ ≅ ∠YXZ

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.

Which statements are correct? Select three options.

△BCD is similar to △BSR.

StartFraction B R Over R D EndFraction = StartFraction B S Over S C EndFraction

If the ratio of BR to BD is , then it is possible that BS = 6 and BC = 3.

(BR)(SC) = (RD)(BS)

StartFraction B R Over R S EndFraction = StartFraction B S Over S C EndFraction

Read the proof.Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°Prove: △HKJ ~ △LNP

CPCTC

definition of supplementary angles

triangle parts relationship theorem

triangle angle sum theorem

Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C.

a reflection and a dilation

a rotation and a dilation

a translation and a dilation

a reflection and a translation

Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F.

a rotation about point A

a reflection across the line containing CB

a reflection across the line containing BA

a rotation about point B

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

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.

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

Option

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

How can ΔABC be mapped to ΔXYZ?

vertex B to vertex Z

vertex B to vertex Y

vertex A to vertex Z

vertex A to vertex Y

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