MATH SOLVE

7 months ago

Q:
# Determine the rigid transformations that will map ΔABC to ΔXYZ.a. Translate vertex B to vertex Z; reflect ΔABC across side AB.b. Translate vertex X to vertex C; rotate ΔXYZ to align the sides and angles.c. Reflect ΔABC across side AB; translate vertex C to vertex X.d. Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

Accepted Solution

A:

Solution: The correct option is d, i.e., Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.Explanation:we know that the sum of angles of a triangle is always [tex]180^{\circ}[/tex]. In ΔXYZ,[tex]\angle X +\angle Y +\angle Z=180^{\circ}[/tex][tex]35^{\circ} +\angle Y +47^{\circ}=180^{\circ}[/tex][tex]\angle Y +82^{\circ}=180^{\circ}[/tex][tex]\angle Y =98^{\circ}[/tex]In both triangles it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A =\angle X=35^{\circ}[/tex] and [tex]\angle B =\angle Y=98^{\circ}[/tex].By AAS rule of congruence ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having same angle and rotate the triangle to align the sides and angles.Since vertex X and vertex A have same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.Hence the correct option is d.