Question

1. 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 if triangles are congruent

Congruent triangles have same size and shape. Use Pythagorean theorem for $\triangle ABC$: $BC=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12$. For $\triangle XYZ$, $YZ=\sqrt{13^{2}-5^{2}} = 12$. So $AC = XZ = 5$, $AB=YX = 13$, $BC=YZ = 12$. Triangles are congruent (same size and shape).

Step2: Determine transformation

$\triangle ABC$ and $\triangle XYZ$: A rotation (to align orientation) and a reflection (to flip as per figure) can map $\triangle ABC$ to $\triangle XYZ$.

Answer:

C. Yes; $\triangle ABC$ maps onto $\triangle XYZ$ with a rotation and a reflection.