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.

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:

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

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

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.

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.

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

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

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

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

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.

Truth Table of a Conditional

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.

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.

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

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

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..

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.

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

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

Homework Pg. 109 1 – 17 all, 18 – 50 EOE