Use Congruent Triangles 1. 2. Objectives: To use congruence shortcuts and CPCTC to show that segments and angles are congruent To construct flowcharts to illustrate the logical flow of an argument Assignment: • P. 166: 12-19 • P. 177-178: 1-11 • Challenge Problems Objective 1 You will be able to use congruence shortcuts and CPCTC to show that segments and angles are congruent Warm-Up Recall that an angle bisector is a ray that divides the angle into two congruent parts. We will use the magic of a compass and straightedge to create one of these divisive rays and then use congruent triangles to explain away that little bit of geometric sorcery. Bisect an Angle 1. Draw an acute angle and label the vertex A. Bisect an Angle 2. Using vertex A as the center, draw an arc intersecting both sides of your angle. Label the intersections B and C. Bisect an Angle 3. Using the same compass setting, draw two intersecting arcs in the interior of your angle, one centered at B, the other centered at C. Bisect an Angle 4. Label the intersection D. Bisect an Angle 5. Draw a ray from vertex A through point D. Example 1 Example 1 Review: Congruence Shortcuts Congruent Triangles (CPCTC) Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent. Corresponding Parts of Congruent Triangles are Congruent Objective 2 You will be able to construct flowcharts to illustrate the logical flow of an argument Flow Chart A flow chart is a concept map that shows a step-bystep procedure through a complicated system. Boxes represent actions, and arrows connect to the boxes to show the flow of action. Example 2 Example 2 1. AC AB Given Given : AC AB CD BD Prove : CAD BAD 2. CD BD Given 3. AD AD Reflexive Property 4. ACD ABD SSS Postulate 5. CAD BAD CPCTC Investigation 1 Within your group, make a flow-chart proof to show that segment AD is congruent to segment BC. Investigation 1 Remember, first show that the triangles are congruent with a shortcut, then use CPCTC to show the segments are congruent. The Proof Game! Round 2 Here’s your chance to play the game that is quickly becoming a favorite among America’s teenagers: The Proof Game! In this round, your group will be given one problem to prove. You are to collaborate with your group members to complete the proof. Then you must choose someone to present said proof to the class. The most significant contributor will earn a delicious reward! Proof Game: Round 2 1. Proof Game: Round 2 2. Proof Game: Round 2 3. Proof Game: Round 2 4. Use Congruent Triangles 1. 2. Objectives: To use congruence shortcuts and CPCTC to show that segments and angles are congruent To construct flowcharts to illustrate the logical flow of an argument Assignment: • P. 166: 12-19 • P. 177-178: 1-11 • Challenge Problems