Chapter 6.5, Problem 5WE

To determine

To complete: the given statement by writing <, $=$ , Or >.

Answer to Problem 5WE

  $m\angle 3>m\angle 4$ .

Explanation of Solution

Given information:

Given figure,

  $\begin{array}{l}m\angle 1---m\angle 2;\\ m\angle 3---m\angle 4\end{array}$

Calculation:

Consider the following data:

  $\overline{AB}\cong \overline{AD}$

And

  $\overline{AC}\cong \overline{AC}$

Then applying Side-Side-Side Inequality,

  $m\angle 1<m\angle 2$

Further sum of all angles in triangle are equal to $180°$ ,

Also, by Isosceles triangle theorem $m\angle ABC=m\angle 3$ and $m\angle ADB=m\angle 4$

Therefore, it is concluded that $m\angle 3>m\angle 4$ .