Chapter 12, Problem 5CA

(a)

To determine

To Prove: The expression $\Delta ABC\cong \Delta DEF$ .

Explanation of Solution

Given Data:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

From the given figure observe that,

  $\overline{BC}\cong \overline{EF}$

The relation for the angle is,

  $\angle B\cong \angle E$

Then, the corresponding length is,

  $\begin{array}{l}\overline{AB}=3\\ \overline{DE}=3\end{array}$

Then,

  $\overline{AB}\cong \overline{DE}$

Then, by the SAS congruence theorem,

  $\Delta ABC\cong \Delta ABC$

Hence, proved.

(b)

To determine

To find: The composition of the rigid motions that maps $\Delta ABC$ to $\Delta DEF$ .

Answer to Problem 5CA

The $\Delta ABC$ is mapped to $\Delta DEF$ and by the translational of the 3 units down and the rotation of $90°$ anti-clockwise.

Explanation of Solution

The objective is to determine composition of the rigid motions that maps $\Delta ABC$ to $\Delta DEF$ .

From the figure it is clear that $\Delta ABC$ is mapped to $\Delta DEF$ and by the translational of the 3 units down and the rotation of $90°$ anti-clockwise.