Chapter 12, Problem 3CA

(a)

To determine

To find: The composition of the transformation that maps $\Delta JKL$ to $\Delta XYZ$ .

Answer to Problem 3CA

The figure $\Delta XYZ$ is the reflection of $\Delta JKL$ in the x axis.

Explanation of Solution

Given Data:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider that the composition of the transformation that map to the $\Delta JKL$ to $\Delta XYZ$ .

The figure shows that $\Delta XYZ$ is the reflection of $\Delta JKL$ in the x axis.

(b)

To determine

To find: Whether the composition is the congruence transformation and then identify the congruent corresponding congruent parts.

Answer to Problem 3CA

The composition is congruence and the congruence parts are $\overline{JK}\cong \overline{XY}$ , $\overline{KL}\cong \overline{YZ}$ and $\overline{JL}\cong \overline{XZ}$ .

Explanation of Solution

From the figure the relation for the sides is,

  $\begin{array}{l}\overline{JK}\cong \overline{XY}\\ \overline{KL}\cong \overline{YZ}\\ \overline{JL}\cong \overline{XZ}\end{array}$

Then, by the SAS congruence theorem,

  $\Delta JKL\cong \Delta XYZ$