Question

lesson 26)
write the converse of this statement and decide whether it is true or false. then, select the correct answer.

if two angles are vertical, then they are congruent.

Explanation:

1. Find the converse: The original statement is in the form "If \( p \), then \( q \)" where \( p \) is "two angles are vertical" and \( q \) is "they are congruent". The converse of "If \( p \), then \( q \)" is "If \( q \), then \( p \)". So we swap the hypothesis (\( p \)) and the conclusion (\( q \)) to get the converse.
2. Determine truth value: There are many pairs of congruent angles that are not vertical (e.g., two 30° angles in different triangles, or two right angles in a rectangle that are adjacent, not vertical). So the statement "If two angles are congruent, then they are vertical" is false.

Answer:

The converse is "If two angles are congruent, then they are vertical", and it is false.