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: Understand translation property

Translation is a rigid transformation. Rigid transformations preserve side - lengths and angle - measures. Corresponding parts of translated (congruent) triangles are congruent.

Step2: Identify corresponding parts

When \(\triangle XYZ\) is translated to get \(\triangle CAB\), the correspondence is \(X\to C\), \(Y\to A\), \(Z\to B\).

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

Answer:

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