Question

PLEASE HEELP

Match the inverse, converse, contrapositive, and biconditional with their sentences.

Conditional Statement: If two angles are congruent, then they have the same measure.

Question 1 options:

converse


biconditional


inverse


contrapositive

1.
If two angles have the same measure, then they are congruent.

2.
If two angles are not congruent, then they do not have the same measure.

3.
If two angles do not have the same measure, then they are not congruent.

4.
Two angles are congruent if and only if they have the same measure.

Answer 1

First, let's define each case:

A conditional statement is:

If P then Q.

P = hypothesis

Q = conclussion.

Converse: If Q then P.

Biconditional: P if and only if Q.

Inverse: If not P, then not Q.

Contrapositive: If not Q, then not P.

Our statement is:

"If two angles are congruent, then they have the same measure."

P = two angles are congruent.

Q = they have the same measure.

Now let's look at the options:

1) If two angles have the same measure, then they are congruent.

or: if Q then P, this is converse.

2) If two angles are not congruent, then they do not have the same measure.

or: If not P, then not Q, this is inverse.

3) If two angles do not have the same measure, then they are not congruent.

or: If not Q, then not P, this is the contrapositive.

4) Two angles are congruent if and only if they have the same measure.

or: P if and only if Q, this is biconditional.