Question

ΔXYZ was reflected to form ΔLMN.

Triangle X Y Z is reflected to from triangle L M N. Angle Z Y X is 86 degrees and angle Y X Z is 38 degrees. Angle L N M is 56 degrees and angle N M L is 86 degrees.

Which statements are true regarding the diagram? Check all that apply.

A. ΔXYZ ≅ ΔLMN
B. ∠Y ≅ ∠M
C. ∠X ≅ ∠L
D. ∠Z ≅ ∠L
E. YZ ≅ ML
F. XZ ≅ LN

Answer 1

True: A, B, C, F.

Reason:
- In ΔXYZ, ∠Y = 86°, ∠X = 38°, so ∠Z = 180 − 86 − 38 = 56°.
- In ΔLMN, ∠N = 56°, ∠M = 86°, so ∠L = 38°.
- A reflection is a rigid motion, so ΔXYZ ≅ ΔLMN (A true).
- The vertex correspondence is X→L, Y→M, Z→N (order preserved), so ∠Y ≅ ∠M (B true), ∠X ≅ ∠L (C true), and XZ corresponds to LN (F true).
- ∠Z ≅ ∠L is false (56° ≠ 38°), and YZ corresponds to MN, not ML, so E is false.