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Geometry 2.3 Law of Syllogism Notes October 24, 2015 Agenda: Law of Syllogism Projects Due!!! - Warm-Up (Writing conditional statements) Big Ideas: - How do we use the Law of Syllogism to draw a logical conclusion? - Writing a two-column proof using algebraic properties to justify our reasoning - HW Quiz #2.2 (Per. 3 only) - Connect the Law of Syllogism to drawing logical conclusions in geometry - Writing a two-column proof 1 Geometry 2.3 Law of Syllogism Notes October 24, 2015 10/22 Warm-Up • For the given statement, write the ifthen form and the converse: Sophomores can take driving lessons. (Hint: If a ________is a _________, then __________________) • Write the 2 conditional statements contained within the following biconditional l statement: Points are coplanar if and only if the points lie on the same plane . 2 Geometry 2.3 Law of Syllogism Notes October 24, 2015 What is a counterexample? An example that shows a statement is false. What is a counterexample that would prove that the converse from our warm-up is false? You can be a freshman and take drivers ed as long as you are 15 3 Geometry 2.3 Law of Syllogism Notes October 24, 2015 Can you think of a counterexample that shows that this is false? 4 Geometry 2.3 Law of Syllogism Notes If If Janelle gets a job Janelle can afford a car. October 24, 2015 ,then Janelle can afford a car. ,then Janelle can drive to school. Therefore, Janelle can drive Janelle gets ,then to school. If a job 5 Geometry 2.3 Law of Syllogism Notes October 24, 2015 If 3x - 4 = 8 ,then 3x = 12 If 3x = 12 ,then x = 4. Therefore, If 3x - 4 = 8 ,then x = 4. 6 Geometry 2.3 Law of Syllogism Notes October 24, 2015 two angles form the two angles If a linear pair ,then are supplementary the sum of the the two angles If are supplementary,then angles is 180 degrees. Therefore, the sum of the two angles form angles is 180 ,then If a linear pair degrees. 7 Geometry 2.3 Law of Syllogism Notes October 24, 2015 If a polygon is regular ,then the polygon is equilateral If a polygon is regular ,then the polygon is equiangular. Why can't we make a valid conclusion? 8 Geometry 2.3 Law of Syllogism Notes Law of Syllogism If P ,then Q If Q ,then R. Therefore, If P ,then R. October 24, 2015 P Q Q R P R 9 Geometry 2.3 Law of Syllogism Notes October 24, 2015 Use the true statements below to determine whether you know if the four conclusions below are true or false. Explain your reasoning. 1. 2. 3. 4. Group Problem - each student complete the problem but work together in your groups one paper per group will be graded... 10