Chapter 4.1, Problem 65STP

To determine

Toexplain:

Type of triangle can serve as a counterexample to the conjecture below.

Answer to Problem 65STP

The correct option is A that is type of triangle is equilateral.

Explanation of Solution

Given information:

If two angles of a triangle are acute, then the measure of the third angle must be greater than or equal to $90$ .

1. Equilateral
2. Obtuse
3. Right
4. scalene

Notice that two angles of the triangle that is equilateral triangle are acute and the third angle of an equilateral triangle is also acute.

This is a counterexample to the conjecture only if two angles of a triangle are acute, then the measure of the third angle must be greater than or equal to $90$ , because the hypothesis is true and the conclusion is false.

So, the triangle in option A describes a counterexample to the given conjecture.

Notice that the third angle in a scalene triangle, is might not be acute. Thus, in a scalene triangle, the conclusion of the given conjecture might be true. So, the triangle in option D does not describes a counterexample to given conjecture.

Hence, the correct option is A.