Question

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

Answer 1

Conditional - a statement that uses the word if.
"Vertical angles are congruent"
Conditional:
If angles are vertical angles, the angles are congruent

Answer 2

thank you :DDD

Answer 3

The three other forms of a conditional:
Inverse: negate the conditional
So if the conditional is "If angles are vertical angles, then the angles are congruent"
Then the inverse would be "If angles are not vertical angles, then the angles are not congruent."

Answer 4

There are also the converse and the contrapositive

Answer 5

Converse - switch around the conditional
"If angles are vertical angles, then the angles are congruent"
"If angles are congruent, then the angles are vertical angles"

Answer 6

Contrapostive: negate the converse

Answer 7

Note: just because you can rearrange a true conditional statement doesn't mean that the resulting statement is also true.

Answer 8

A conditional exists in the form:
If p, then q

Inverse:
If ~p, then ~q
(where the ~ sign indicates negation)

Converse:
If q, then p

Contrapositive:
If ~q, then ~p

Answer 9

ok thank you :)

Answer 10

Yep :)