Question

triangle xyz was translated up 2 and right 3 units, creating triangle cab. which relationship between the parts of the two triangles must be true?

∠x ≅ ∠a

\overline{zx} ≅ \overline{ca}

\overline{yz} ≅ \overline{ab}

∠z ≅ ∠c

Explanation:

Step1: Recall the property of translation

Translation is a rigid transformation. Rigid transformations (translations, rotations, reflections) preserve the shape and size of the figure. So, the pre - image (\(\triangle XYZ\)) and the image (\(\triangle CAB\)) are congruent, i.e., \(\triangle XYZ\cong\triangle CAB\).

Step2: Use the congruence of triangles

If \(\triangle XYZ\cong\triangle CAB\), then the corresponding parts of congruent triangles are congruent (CPCTC).

• For angles: \(\angle X\cong\angle C\), \(\angle Y\cong\angle A\), \(\angle Z\cong\angle B\)
• For sides: \(\overline{XY}\cong\overline{CA}\), \(\overline{YZ}\cong\overline{AB}\), \(\overline{ZX}\cong\overline{BC}\)

Answer:

\(\overline{YZ}\cong\overline{AB}\)