Question

3. Start with the following statement: Vertical angles are congruent. a. State the conditional and three other forms of the statement. b. Write all 4 forms of the statement using symbols. c. If you know that a statement is true, what do you know about the truth of its converse, inverse, and contrapositive? BONUS: Use at least one truth table AND at least one property to support your reasoning.

Answer 1

Four statements driven from the original: converse: if a pair of angles are congruent, then the angles are vertical. inverse: if a pair of angles are not vertical, then the angles are not congruent. contrapositive: if a pair of angles are not congruent, then the angles are not vertical. conditional: if a pair of angles are vertical, then the angles are congruent. b) If you know that a statement is true, then its contrapositive form must be true as well.