Chapter 7, Problem 21RP

a.

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Answer to Problem 21RP

Always True.

Explanation of Solution

Given:

The following is the given statement-

An equilateral triangle is isosceles.

Calculation:-

The statement is always True because in equilateral triangle all sides are equal and in isosceles any two sides need to be equal.

b.

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Answer to Problem 21RP

Sometimes True.

Explanation of Solution

Given:

The following is the given statement-

The number of diagonals in the polygon is the same as the number of sides.

Calculation:-

The number of sides will only equal the number of diagonals if the figure is a pentagon. In all other figures, the number of sides will never equal the number of diagonals.

c.

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Answer to Problem 21RP

Sometimes True.

Explanation of Solution

Given:

The following is the given statement-

An exterior angle of a triangle is larger in measure than any angle of a triangle.

Calculation:-

If the triangle is acute, the the exterior angle will be obtuse, and larger than any angle in the triangle. However, if the triangle is obtuse, then the exterior angle of the obtuse angle is acute, and therefore smaller than the obtuse angle

d.

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Answer to Problem 21RP

Never True.

Explanation of Solution

Given:

The following is the given statement-

One of the base angles of an isosceles triangle has a measure greater than that of one of the exterior angles of the triangle.

Calculation:-

If the triangle is isosceles, then the base angle has to be less than $90$ degrees, because otherwise the measure of the angles of the triangle would be larger than $180$