Question

does △abc appear to be the same size and shape as △xyz? explain
a yes, △abc maps onto △xyz with a translation and a rotation
b yes, △abc maps onto △xyz with a translation and a reflection
c yes, △abc maps onto △xyz with a rotation and a reflection
d no, the triangles are different sizes

Explanation:

Step1: Check side - length equality

In \(\triangle ABC\), \(AC = 5\), \(AB=13\). In \(\triangle XYZ\), \(XZ = 5\), \(XY = 13\). Also, \(\angle C=\angle Z = 90^{\circ}\). By the Hypotenuse - Leg (HL) congruence criterion for right - triangles (if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, the two right - triangles are congruent), \(\triangle ABC\cong\triangle XYZ\).

Step2: Analyze transformation

To map \(\triangle ABC\) onto \(\triangle XYZ\), first, we note that the orientation of the triangles is different. We can rotate \(\triangle ABC\) to align the general shape and then reflect it to get the exact orientation.

Answer:

C. Yes, \(\triangle ABC\) maps onto \(\triangle XYZ\) with a rotation and a reflection