Chapter 8, Problem 9CUR

a)

To determine

To write: a statement that is logically equivalent to the given conditional.

Answer to Problem 9CUR

If $\Delta$ is equiangular then it is isosceles.

Explanation of Solution

Given Information:

Given statement,

A triangle is equiangular only if it is isosceles.

Calculation:

Consider the following statement.

A triangle is equiangular only if it is isosceles.

It is required to rewrite the above in the form, “if, then”

Since both the conditions are dependent on each other so it can be written in two form.

“If $\Delta$ is equiangular then it is isosceles”.

b)

To determine

To state: the converse and to sketch a diagram to disprove the converse.

Explanation of Solution

Given Information:

Given statement,

A triangle is equiangular only if it is isosceles.

Calculation:

Consider the following statement.

“If $\Delta$ is equiangular then it is isosceles”.

It is required to write the converse of the above statement.

The converse of the statement is given below.

“If $\Delta$ is isosceles, then it is equiangular”.

For example, in the below figure, $ABC$ is an isosceles triangle.

In this triangle, only two angles are equal, so it is not an equiangular triangle.