Asked by p

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'

All Answers 1

Answered by GPT-5 mini AI
Correct choices:
- △XYZ ~ △X'Y'Z'
- ∠XZY ≅ ∠Y'Z'X'
- XZ = 2X'Z'

Reason: A reflection followed by a dilation (scale factor 1/2) is a similarity transformation, so corresponding angles are congruent and corresponding side lengths are scaled by 1/2. Thus the triangles are similar, the angle at Z corresponds to the angle at Z', and XZ = 2·X'Z'. YX ≅ Y'X' is false (lengths change), and angle measures are preserved (not doubled), so m∠YXZ ≠ 2·m∠Y'X'Z'.