Question

Given the conditional statement, match the following items.

Conditional statement: If two angles are adjacent, then the two angles have the same vertex.

1 If two angles have the same vertex, then they are adjacent.


2 If two angles are not adjacent, then the angles to not have the same vertex
 
. 3 If two angles do not have the same vertex, then the two angles are not adjacent.

Contrapositive, Converse,  Inverse

Answer 1

1 is the Converse,
2 is the Inverse
3 is the Contrapositive

Answer 2

1) Converse statement.

2) Inverse statement.

3) Contrapositive statement.

Explanation:

We are given a conditional statement as:

Conditional statement:

If two angles are adjacent, then the two angles have the same vertex.

1)

We know that for any statement of the type:

If p then q

The converse of the statement is:

if q then p

Hence, the converse statement is:

If two angles have the same vertex, then they are adjacent.

2)

We know that for any statement of the type:

If p then q

The inverse of the statement is:

If not p then not q

Hence, the inverse of the given conditional statement is:

If two angles are not adjacent, then the angles to not have the same vertex.

3)

If we switch our hypothesis and conclusion of the given conditional statement and negate both of them then we obtain a contrapositive statement.

Hence, the contrapositive statement of the given conditional statement is:

If two angles do not have the same vertex, then the two angles are not adjacent.