For each statement

1. tell whether the statement is true or false,
2. write the converse,
3. tell whether the converse is true or false.

If two lines are perpendicular, then they form congruent adjacent angles.

Adjacent angles are angles that come out of the same vertex. Vertical angles are always congruent, which means that they are equal.

When two lines are perpendicular, then they form four angles each measuring$90°$

So, all the adjacent angles are congruent.

From first and second statement given statement is true.

Converse of a statement “if $P$ then $Q$” is “if$Q$ then $P$”

P is “lines are perpendicular”

Q is “congruent adjacent angles”

If two lines intersect to form congruent adjacent angles, then the lines are perpendicular

Adjacent angles are angles that come out of the same vertex. Vertical angles are always congruent, which means that they are equal.

The sum of all the angles when two intersect is $360°$. If the adjacent angles are congruent, then the measure of each angle is $90°$. That means, the lines are perpendicular.

From first and second statement given statement is true.