Conditional Statements and the Converse Geometry Unit 11, Day 7 Ms. Reed.

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Presentation transcript:

Conditional Statements and the Converse Geometry Unit 11, Day 7 Ms. Reed

Definition A Conditional Statement is a statement that can be written in if-then form. Example: If you come late to class twice, then you get a detention

Conditional Statements Using symbols, if p then q would be written as p  q. The phrase after the word “if” is the hypothesis. (p) The phrase after the word “then” is the conclusion. (q) p  q is read “if p then q” or “p implies q”

State the Hypothesis and Conclusion of the following: 1. If points A, B, and C lie on line l, then they are collinear. 2. The Tigers will play in the tournament if they win their next game.

Truth Value of Conditional The truth value of a conditional statement is true in all cases EXCEPT when the hypothesis is true and the conclusion is false. (T  F) Look at the example in your notes packet.

Truth Table for Conditional Statements pqpqpq TT TF FT FF

Definition Converse – Exchanging the hypothesis and conclusion of the conditional. Ex. Conditional: If two angles have the same measure, then they are congruent. Converse: If two angles are congruent, then they have the same measure.

Conditional to Converse Conditional: p  q Converse: q  p Conditional: ~p  q Converse: q  ~p Conditional: ~q  ~p Converse: ~p  ~q

Truth Table for Converse pq Conditional p  q Converse q  p TT TF FT FF

Class Work: Identify the hypothesis and conclusions: If a polygon has six sides, then it is a hexagon. Write the statement in if-then form: An angle formed by perpendicular lines is a right angle.

Class Work (cont.): Determine the truth vales of the following statements for each set of conditions. If you drive faster than 65 mph on the interstate, then you will receive a speeding ticket. 1. You drive 70 mph, and you receive a speeding ticket. 2. You drive 62 mph, and you do not receive a speeding ticket. 3. You drive 68 mph, and you do not receive a speeding ticket.

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