Chapter 12.1, Problem 44E

To determine

To find: whether it is possible to draw a right isosceles triangle and right equilateral triangle with proper explanation.

Answer to Problem 44E

Right isosceles triangle exists and right equilateral does not exist.

Explanation of Solution

Given:

Right isosceles triangle and right equilateral.

Concept used:

Sum of the three interior angles of triangle is always ${180}^0$ .

Isosceles triangle will have same $2$ side and one base.

Every equilateral triangle has all three angles with measure ${60}^0$ .

Calculation:

Right isosceles triangle exists.

Example:

  

  $\begin{array}{l}x+45+45={180}^0.\\ x={90}^0.\end{array}$

Every equilateral triangle has all three angles with measure ${60}^0$ ,meaning that right equilateral triangle does not exist.

Hence,right isosceles triangle exists and right equilateral does not exist.