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 ZX ≅ CA YZ ≅ AB ∠Z ≅ ∠C

Answer 1

YZ ≅ AB

Step-by-step explanation:

A translation is known as a rigid transformation. This is because it preserves congruence. Since CAB is created from XYZ, this tells us that:

X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.

Since the triangles are congruent, the corresponding pieces are congruent as well.

Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.

Answer 2

Triangle XYZ is moved up 2 and right 3 units and the new triangle CAB is create.

So,

X = C, Y = A and Z = B and

XY ≅ CA, YZ ≅ AB and ZX ≅ BC.

Hence, in the given options, the correct relationship is:

YZ ≅ AB.