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, \(\triangle XYZ\cong\triangle CAB\).

Step2: Use the congruent - triangle property (CPCTC: Corresponding Parts of Congruent Triangles are Congruent)

If \(\triangle XYZ\cong\triangle CAB\), then:

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

Answer:

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