Question

δxyz was reflected over a vertical line, then dilated by a scale factor of \\(\frac{1}{2}\\), resulting in δxyz. which must be true of the two triangles? select three options.\
\\(\square\\) δxyz ~ δxyz\
\\(\square\\) \\(\angle xzy \cong \angle yzx\\)\
\\(\square\\) \\(\overline{yx} \cong \overline{yx}\\)\
\\(\square\\) \\(xz = 2xz\\)\
\\(\square\\) \\(m\angle yxz = 2m\angle yxz\\)

Explanation:

Step1: Analyze transformations

Reflection preserves shape/size; dilation preserves shape (similarity).

Step2: Check similarity

Similarity requires same shape (reflection+dilation → yes).

Step3: Check angle congruence

Reflections/dilations preserve angle measures.

Step4: Check side length relation

Dilation scale factor $\frac{1}{2}$ → original side = 2×dilated side.

Answer:

△XYZ ~ △X'Y'Z', ∠XZY ≅ ∠Y'Z'X', XZ = 2X'Z'