Question

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If two lines intersect to form right angles, then the lines are perpendicular.

Short answer

The given statement is true.

The converse is stated as follows:

If two lines are perpendicular, then the lines intersect to form right angles.

The converse statement is also true.

Step-by-step solution

Step 1. Define perpendicular lines. 

When two lines meet each other at right angles. The lines are said to be perpendicular to each other.

Step 2. State the explanation.

Here, uses the fact that perpendicular lines are lines that intersect at a right (90degrees) angle.

So,the given statement is true.

Converse statement is as follows:

If two lines are perpendicular, then the lines intersect to form right angles.

Step 3. State the conclusion.

Therefore, the given statement is true and converse of the statement is also true.