Question

Triangle X Y Z is translated up 2 and right 3 units to form triangle C A B.
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
ZX ≅ CA
YZ ≅ AB
∠Z ≅ ∠C

Answer 1

YZ ≅ AB.

A translation is a rigid motion, so it preserves distances. Since the translation sends Y → A and Z → B, segment YZ corresponds to AB and must be congruent to it.