1. Lesson 2 – 3 Conditional Statements
Geometry
Lesson 2 – 3
Conditional Statements
Objective:
Analyze statements in if-then form.
Write the converse, inverse, and contrapositive of if-then statements.

2. Conditional Statement
Conditional Statement – a statement that can be written in if-then form.
If you would like to speak to a representative, then you should press 0 now.
If-then statement (same as conditional statement)
if p, then q
A conditional statement (or if-then statement) written in math symbols:

3. Parts of a Conditional Statement
Hypothesis – the phrase following if
If you would like to speak to a representative, then you should press 0 now.
p is the hypothesis
Conclusion – the phrase following then
q is the conclusion

4. Identify the Hypothesis and Conclusion
If the forecast is rain, then I will take an umbrella.
2 options on homework: H C
H: the forecast is rain
C: I will take an umbrella

5. Identify the Hypothesis and Conclusion
A number is divisible by 10 if its last digit is a 0.
Not written in ‘normal’ if-then form.
Find the hypothesis first.
Can you find the conclusion?
H: its last digit is a 0
C: a number is divisible by 10
Can be rewritten as:
If a numbers last digit is a 0, then it is divisible by 10.
Can’t have ‘it’ as a subject so must reword the sentence.

6. Identify the Hypothesis and Conclusion
If a polygon has six sides, then it is a hexagon.
Another performance will be scheduled if the first one is sold out.
H: a polygon has six sides
C: it is a hexagon
H: the first one is sold out
C: another performance will be scheduled
Can be rewritten as:
If the first performance is sold out, then another one will be scheduled.

7. A mammal is a warm-blooded animal.
Identify the hypothesis and conclusion for each conditional statement. Then write the statement in if-then form.
A mammal is a warm-blooded animal.
On homework: write in if-then then underline H & C
If an animal is a mammal, then it is warm-blooded. H C

8. A prism with bases that are regular polygons is a regular prism.
If a prism has bases that are regular polygons,
then it is a regular polygon. H C

9. Four quarters can be exchanged for a $1 bill.
If you have four quarters, then you can exchange
them for a $1 bill. H C

10. The sum of the measures of two supplementary angles is 180.
If two angles are supplementary, then their sum is 180. H C

11. Real World Conditional
If Tom finishes his homework, then he will clean his room.
When the hypothesis of a conditional is not met, the truth of a
Conditional cannot be determined. When it cannot be determined,
it is considered true by default.

12. Truth Table of a Conditional

13. If next month is August, then this month is July.
Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counter example.
If you divide an integer by another integer, the result is also an integer.
If next month is August, then this month is July.
False: 1 / 2 = 0.5 which is not an integer.
True, If next month is Aug. then this month would have to be July.

14. If a triangle has four sides, then it is concave.
If angle A is an acute angle, then measure of angle A is 35.
TRUE. Even though we know a triangle cannot have 4 sides and the
hypothesis is False the overall conditional is true since all if-then
statements with F hypothesis's are True
False, measure of angle A could be 55.
True, since the square root of a number cannot be negative the
Hypothesis is false which makes the whole statement true.

15. Related Conditionals Conditional Converse Inverse Contrapositive
H becomes C and
C becomes H
The negation of the
conditional
The negation of
inverse

16. Logically Equivalent Statements with the same truth values
A conditional and its contrapositive are logically equivalent
The converse and inverse are logically equivalent.

17. Lions are cats that can roar. Information from book:
Write the converse, inverse, and contrapositive of the following statement. Then tell whether each is T or F. If false, give a counterexample.
Lions are cats that can roar.
Information from book:
Cats in the genus Panthera include the leopard, jaguar, lion, and tiger. These are the only cats that can roar. They cannot, however, purr.
Conditional:
If a cat is a lion, then it can roar.
Cont..

18. If a cat can roar, then it is a lion.
Lions are cats that can roar. Information from book: Cats in the genus Panthera include the leopard, jaguar, lion, and tiger. These are the only cats that can roar. They cannot, however, purr.
Converse:
Inverse:
Contrapositive:
If a cat can roar, then it is a lion.
False, it could be a tiger.
If a cat is not a lion, then it cannot roar.
False, it could be a tiger that can roar.
If a cat cannot roar, then it is not a lion.
True, if the cat cannot roar then it can’t be a lion.

19. Two angles that have the same measure are congruent.
Write the converse, inverse, and contrapostive of each true condtional statement. Determine whether each related conditional is T or F. If a statement is false, find a counterexample.
Two angles that have the same measure are congruent.
Conditional:
If two angles have the same measure, then they are congruent.
Converse:
If two angles are congruent, then they have the same measure.
True

20. Two angles that have the same measure are congruent.
Inverse:
If two angles do not have the same measure, then they are not congruent.
True
Contrapositive:
If two angles are not congruent, then they do not have the same
measure.
True

21. Homework
Pg – 17 all, 18 – 50 EOE