Chapter 4.4, Problem 4CE

To determine

To find:The statements that are true for the given isosceles triangles.

  $\begin{array}{l}\text{a}\text{. }\angle D\cong \angle R\text{ b}\text{. }\overline{DE}\cong \overline{DF}\text{ c}\text{. }\overline{DF}\cong \overline{RT}\\ \text{d}\text{. }\angle E\cong \angle F\text{ e}\text{. }\angle E\cong \angle S\text{ f}\text{. }\angle S\cong \angle T\end{array}$

Answer to Problem 4CE

The true statements are:

  $\begin{array}{l}\overline{DE}\cong \overline{DF}\\ \overline{DF}\cong \overline{RT}\\ \angle E\cong \angle F\\ \angle S\cong \angle T\end{array}$

Explanation of Solution

Given information:Two isosceles triangles.

  

Concept/Formula used:In an isosceles triangle, any two sides are always congruent. And angles opposite to these equal opposite sides are also congruent.

Calculation: From the isosceles triangles, it can be seen that $\overline{DE}=\overline{RT}=8\text{ cm}$ . Thus, $\overline{DE}\cong \overline{RT}$ .

In $\Delta DEF$ , as $\overline{DE}\cong \overline{DF}$ , so $\angle E\cong \angle F$ .

Similarly, in $\Delta RST$ , $\overline{RS}\cong \overline{RT}$ , so, $\angle S\cong \angle T$ .

Conclusion: Hence, the statements that are true are:

  $\begin{array}{l}\overline{DE}\cong \overline{DF}\\ \overline{DF}\cong \overline{RT}\\ \angle E\cong \angle F\\ \angle S\cong \angle T\end{array}$