Chapter 6.5, Problem 62SPR

To determine

The transformation given in the figure.

Answer to Problem 62SPR

  $\Delta ABC\cong \Delta XYZ$ , as all three corresponding sides are congruent to each other.

Explanation of Solution

Given:

The given figure is:

  

Calculation:

A reflection of an object is the transformation over a line. The distance of the pre-image and its image are at the same distance.

In the given figure, triangle XYZ is the reflection of triangle ABC.

Therefore, finding the sides of triangle ABC;

  $\begin{array}{l}AB=5,BC=4\\ So,\\ AC=\sqrt{{\left(AB\right)}^2+{\left(BC\right)}^2}\\ AC=\sqrt{{\left(5\right)}^2+{\left(4\right)}^2}\\ AC=\sqrt{41}\end{array}$

Now, finding the sides of triangle XYZ;

  $\begin{array}{l}XY=5,YZ=4\\ So,\\ XZ=\sqrt{{\left(XY\right)}^2+{\left(YZ\right)}^2}\\ XZ=\sqrt{{\left(5\right)}^2+{\left(4\right)}^2}\\ XZ=\sqrt{41}\end{array}$

According to the SSS Congruence, $\Delta ABC\cong \Delta XYZ$ , as all three corresponding sides are congruent to each other.