Conditional Statements A conditional statement is a statement that can be written in “if-then” form. The hypothesis of the statement is the phrase immediately.

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Conditional Statements A conditional statement is a statement that can be written in “if-then” form. The hypothesis of the statement is the phrase immediately following the word “if”. The conclusion is the phrase following “then”. Example: If our team wins Friday night, then we will be the state champions. Hypothesis: our team wins Friday night Conclusion: we will be the state champions

We use symbols to represent the parts of a conditional statement. We use the letter p to represent the hypothesis, and the letter q to represent the conclusion. We may need more letters if there are several statements to be considered. Using these symbols, we can write the following: p→q which mean “if p then q” or “p implies q”

If points A, B, and C lie on line m, then they are collinear. Hypothesis: Conclusion: The Tigers will play in the tournament if they win their next game. p: q:

An angle with measure greater than 90 is an obtuse angle. Now we rewrite the statement in “if-then” form: Hypothesis: Conclusion:

Perpendicular lines intersect. Now we rewrite the statement in “if-then” form: Sometimes we must add information to put the statement into true conditional format.

Example 3-1a Identify the hypothesis and conclusion of the following statements. 1) If a polygon has 6 sides, then it is a hexagon. 2) If you are a baby, then you will cry. 3) To find the distance between two points, you can use the Distance Formula.

Example 3-2a Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. 1) Distance is positive. 2) A five-sided polygon is a pentagon.

Example 3-2c Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form. a. A polygon with 8 sides is an octagon. b. An angle that measures 45º is an acute angle.

Other Forms of Conditionals Converse: Reverse the hypothesis and conclusion in a conditional statement. For example: Notice that when a conditional is true, the converse may not be true. In geometry, we will always be striving to examine statements to determine if they are true and if their converse is also true. In symbols, if the conditional is p → q, then the converse is q → p. Conditional: If it rained today, then my yard got wet. Converse: If my yard got wet, then it rained today.

Example 3-4a 1)Write the converse, of the statement All squares are rectangles. 2)Determine whether each statement is true or false. If a statement is false, give a counterexample. Conditional: Converse:

Example 3-4b 1)Write the converse of the statement The sum of the measures of two complementary angles is 90. 2)Determine whether each statement is true or false. If a statement is false, give a counterexample.

Example 3-4b 1)Write the converse of the statement Linear pairs of angles are supplementary. 2)Determine whether each statement is true or false. If a statement is false, give a counterexample.