Chapter 4.6, Problem 28PPS

To determine

The conjecture about the relationship between base angles of an isosceles right triangle.

Explanation of Solution

The conjecture will be:

The base angles of an isosceles right triangle are of measure 45.

Let EGH be an isosceles right triangle.

  

Here, angle EHG is 90 degrees.

According to Isosceles Triangle Theorem, if two sides of a triangle are congruent, then the angles that are opposite to those 2 sides are also congruent.

Therefore,

  $\begin{array}{l}\angle G\cong \angle E;\\ m\angle G=m\angle E\end{array}$

The acute angles in a right triangle are complementary.

  $\begin{array}{l}m\angle G+m\angle E=90\\ 2\left(m\angle G\right)=90\\ m\angle G=\frac{90}{2}\\ m\angle G=45\end{array}$

Hence, this proves the conjecture.