Question

How can ΔABC be mapped to ΔXYZ?

Triangles A B C and X Y Z are shown. The lengths of sides A B and X Y are 25 centimeters. The lengths of sides A C and X Z are 29 centimeters. Angles B A C and Y X Z are 36 degrees. Triangle A B C is slightly higher and to the left of triangle X Y Z. Triangle A B C is rotated to form triangle X Y Z.

First, translate ____________________. Next, rotate ΔABC about B to align the sides and angles.

vertex B to vertex Z
vertex B to vertex Y
vertex A to vertex Z
vertex A to vertex Y

Answer 1

To map triangle ΔABC to triangle ΔXYZ by translating first and then rotating, you should follow these steps:

1. **Translate** triangle ΔABC so that vertex **B** coincides with vertex **Z**. This is necessary because the sides AB and XY are aligned and we want them to overlap correctly for the next step.

2. Next, **rotate** triangle ΔABC about vertex B to align the sides and angles with triangle ΔXYZ.

So, the complete sentence would be:

"First, translate **vertex B to vertex Z**. Next, rotate ΔABC about B to align the sides and angles."