Chapter 4, Problem 2CT

To determine

To complete: the blank in the given statement.

Answer to Problem 2CT

$\overline{EG}$ ; $\overline{FG}$ ; 43

Explanation of Solution

Given information:

The given statement is “ $\Delta EFG$ is isosceles, with $m\angle G=94$ . The legs are sides

$\underset{\_}{}$ and $\underset{\_}{}$ . $m\angle E=\underset{\_}{}$ ”.

The isosceles triangle has two equal sides and two equal angles.

If two angles of the triangle will be 94 degrees, then it will not satisfy the angle sum property of the triangle.

So, $\angle G$ is the non-congruent angle and the other two angles are congruent.

The legs are sides $\overline{EG}\&\overline{FG}$ .

  $\begin{array}{l}m\angle E+m\angle F+m\angle G=180\\ m\angle E+m\angle E+94=180\\ 2m\angle E=180-94\\ \Rightarrow m\angle E=m\angle F=\frac{180-94}{2}=43\end{array}$

Hence,

The legs are sides $\underset{\_}{\overline{EG}}$ and $\underset{\_}{\overline{FG}}$ . $m\angle E=\underset{\_}{\text{ 43 }}$ .