Chapter 12.1, Problem 43E

To determine

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

Answer to Problem 43E

The obtuse isosceles triangle exists and obtuse equilateral triangle does not exist.

Explanation of Solution

Given:

Obtuse isosceles triangle and obtuse equilateral.

Concept used:

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

Obtuse triangles are those triangles which has one angle obtuse greater than ${90}^0$ .

Equilateral triangle must have angle of ${60}^0$ each angle.

Calculation:

Obtuse isosceles triangle exists.

Example:

  $\begin{array}{l}x+30+30={180}^0.\\ x={120}^0.\end{array}$

If one angle of triangle is greater than ${90}^0$ ,other two angle is same so, the triangle is also isosceles.

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

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