Question

1. if 2 angles are vertical, then they are congruent. true or false? converse: true or false? inverse: true or false? contrapositive: true or false?

Explanation:

Step1: Recall vertical - angle property

Vertical angles are always congruent. So the statement "If 2 angles are vertical, then they are congruent" is True.

Step2: Find the converse

The converse of "If p, then q" is "If q, then p". Here, p = "2 angles are vertical" and q = "they are congruent". The converse is "If 2 angles are congruent, then they are vertical". This is False because congruent angles can have different positions and not be vertical angles.

Step3: Find the inverse

The inverse of "If p, then q" is "If not p, then not q". The inverse is "If 2 angles are not vertical, then they are not congruent". This is False since non - vertical angles can be congruent.

Step4: Find the contrapositive

The contrapositive of "If p, then q" is "If not q, then not p". The contrapositive is "If 2 angles are not congruent, then they are not vertical". This is True because vertical angles are always congruent, so non - congruent angles cannot be vertical.

Answer:

Statement: True
Converse: If 2 angles are congruent, then they are vertical. False
Inverse: If 2 angles are not vertical, then they are not congruent. False
Contrapositive: If 2 angles are not congruent, then they are not vertical. True