1. Conditional Statements

2. Objectives Write statements in if-then form.
Write the converse, inverse, and contrapositive of if-then statements.

3. Statements A statement is any sentence.
Statements are most often represented using a letter such as p or q.
Example: p: A triangle has 3 sides.
q: Triangular polygons have 3 sides.

4. If-Then Statements If 3, then p q
A conditional statement is a statement that can be written in if-then form. Example: If an animal has hair, then it is a mammal.
Conditional statements can be written as “if p, then q.”
We write p q using symbols, which is read “if p, then q” or “p implies q.”
If 3, then p q

5. Hypothesis and Conclusions
Hypothesis is the IF part of a conditional statement.
Conclusions are the THEN part of a conditional statement.
If a triangle, then 3 sides.
hypothesis
conclusion

6. Example 1:
Identify the hypothesis and conclusion of the following statement.
Tamika will advance to the next level of play if she completes the maze in her computer game.
Write in IF, THEN form first…..

7. Example 2:
Write each statement in if-then form. Identify the hypothesis and conclusion of each statement..
a. A polygon with 8 sides is an octagon.
b. An angle that measures 45º is an acute angle.

8. Converse, Inverse, and Contrapositive
Statement
Formed by
Symbols
Examples
Conditional
If , then
p q
If 2 angles have the same measure, then they are congruent.
Converse
Switch p and q
q p
If 2 angles are congruent, then they have the same measure.
Inverse
Nots to p and q
~p ~q
If 2 angles do not have the same measure, then they are not congruent.
Contrapositive
Switch and Nots to p and q
~q ~p
If 2 angles are not congruent, then they do not have the same measure.

9. Converse, Inverse, and Contrapositive
If 3, then
Converse: Switch
Inverse: Add nots
Contrapositive: Switch and add nots

10. Example 4:
Write the converse, inverse, and contrapositive of the statement All squares are rectangles.
Conditional: If a shape is a square, then it is a rectangle.
Converse:

11. Example 4:
Inverse:
Contrapositive:

12. Your Turn:
Write the converse, inverse, and contrapositive of the conditional statement If the two angles are complementary, then the sum of their measures is 90
Inverse:
Converse:
Contrapositive:

13. Assignment
Geometry Workbook, pages