Chapter 4.7, Problem 5CYU

To determine

Each transformation and to verify that it is a congruence transformation.

Answer to Problem 5CYU

By SSS Congruence Postulate, both the triangles are congruent.

Explanation of Solution

Given:

The given figure is:

  

Calculation:

Reflection is a transformation over a line. Each point on the original figure and reflected figure are at the same distance from the line of reflection.

In given figure, the points of triangles LKJ and XYZ are at the equal distance from the line of reflection. Hence, LKJ is a reflection of XYZ.

The lengths of sides of XYZ are:

  $XY=7,YZ=8$

The length of XZ is:

  $\begin{array}{l}XZ=\sqrt{{\left(XY\right)}^2+{\left(YZ\right)}^2}\\ XZ=\sqrt{7^2+8^2}\\ XZ=\sqrt{113}\end{array}$

The lengths of sides of LKJ are:

  $KL=7,KJ=8$

The length of LJ is:

  $\begin{array}{l}LJ=\sqrt{{\left(KL\right)}^2+{\left(KJ\right)}^2}\\ LJ=\sqrt{7^2+8^2}\\ LJ=\sqrt{113}\end{array}$

By SSS Congruence Postulate, both the triangles are congruent.