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.

Answer 1

To map ΔABC to ΔXYZ, first translate ΔABC along the vector from B to Y, then rotate it about point B to align everything with ΔXYZ.

Step-by-step explanation:

To map ΔABC to ΔXYZ, we need to perform a series of transformations, specifically a translation followed by a rotation. Given that sides AB and XY, and sides AC and XZ are equal in length, as well as angles BAC and YXZ being equal, we can deduce that these triangles are congruent.

First, translate ΔABC along the vector that connects points B and Y. This will position point B on point Y without altering the size or shape of ΔABC. Next, rotate ΔABC about point B (now coinciding with point Y) until side BA aligns with YX and side BC aligns with YZ. This rotation should be done in such a way that ΔABC is placed exactly over ΔXYZ, matching all corresponding sides and angles.