Question

Triangles X Y Z and X prime Y prime Z prime are shown.
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.

△XYZ ~ △X'Y'Z'
AngleXZY ≅ AngleY'Z'X'
YX ≅ Y'X'
XZ = 2X'Z'
mAngleYXZ = 2mAngleY'X'Z'

Answer 1

Correct choices (with brief reasons):

- △XYZ ~ △X'Y'Z' — Reflection + dilation produces a similar triangle.
- ∠XZY ≅ ∠Y'Z'X' — Reflections and dilations preserve angle measures.
- XZ = 2 X'Z' — Dilation scale factor 1/2 makes each corresponding side half as long, so the original side is twice the image.

The other two are false: corresponding sides are not congruent (they're half), and angles are preserved (not doubled).