Question

Write four true conditional statements based on this biconditional statement.

An angle is a right angle if and only if it measures 90°.

Answer 1

The four true statements are:

1. If an angle is a right angle, it measures 90°.

2. If an angle measures 90°, it is a right angle.

3. If an angle is not a right angle, it does not measure measure 90°.

4. If an angle does not measure 90°, it is not a right angle.

Explanation:

Given the biconditional statement:

An angle is a right angle if and only if it measures 90°.

To find:

Four true conditional statements.

Solution:

First of all, let us the learn the concept of four true conditional statements from a given biconditional statement.

Let the biconditional statement be "
`a` is true if and only if
`b` is true.

Then the four true statements can be written as:

1. If
`a` is true then
`b` is true.

2. If
`b` is true then
`a` is true.

3. If
`a` is false then
`b` is false.

4. If
`b` is false then
`a` is false.

Here
`a` is "an angle is a right angle"

`b` is "it measures 90°" .

So, the four true statements are:

1. If an angle is a right angle, it measures 90°.

2. If an angle measures 90°, it is a right angle.

3. If an angle is not a right angle, it does not measure measure 90°.

4. If an angle does not measure 90°, it is not a right angle.