The document defines and provides examples of the converse, inverse, and contrapositive of conditional statements. The converse is formed by interchanging the hypothesis and conclusion of a conditional statement. The inverse is formed by negating both the hypothesis and conclusion. The contrapositive is logically equivalent to the original statement and is formed by switching the hypothesis and conclusion and stating their opposites. Examples are provided to illustrate each type of statement transformation.

1. CONVERSE,
INVERSE, and
CONTRAPOSITIVE
STATEMENT

2. The CONVERSE of a
conditional statement is
formed by interchanging the
hypothesis and conclusion.

3. 1. IF two angles are adjacent,
THEN they have a common
vertex.
CONVERSE - IF two angles
a common vertex, THEN they
are adjacent.

4. 2. IF two angles are
supplementary, THEN the sum of
their angles is 180 degrees.
CONVERSE - IF two angles have a
sum of 180 degrees, THEN they
are supplementary.

5. 3. IF you are 5 feet tall,
you are also 60 inches tall.
CONVERSE - IF you are 60
inches tall, THEN you are
feet tall.

6. Given a conditional
statement, its INVERSE can
be formed by negating both
the hypothesis and
conclusion.

7. Inverse: State the opposite of both
the hypothesis and conclusion.
If two angles are vertical,
then they are congruent.
Inverse: If two angles are
vertical, then they are not
congruent.

8. Given a conditional
statement, its
CONTRAPOSITIVE are
logically equivalent to
the original conditional
statement.

9. Contrapositive: Switch the
hypothesis and conclusion and
state their opposites.
If two angles are vertical, then
they are congruent.
If two angles are not congruent,
then they are not vertical.

10. Statement: A triangle is a polygon.
If-then form: If a shape is a triangle, then it
is a polygon.
Converse: If it is a polygon, then it’s shape is a
triangle.
Inverse: If a shape is not a triangle, then it is
not a polygon.
Contrapositive: If a shape is not a polygon,
then it is not a triangle.

11. 1. All right angles are equal.
2. A segment has exactly one
midpoint.
3. Angles in a linear pair are
supplementary.
4. Pentagon has five sides.
5. Drinking Pepsi makes you happy.