Question

Write four true conditional statements based on this biconditional statement.

Answer 1

Answer:

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.

Step-by-step 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.