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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 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. Bisect an Angle Video Click on the button below to watch a video on how to bisect an angle 4.6 Use Congruent Triangles Objectives: 1. To use congruence shortcuts and CPCTC to show that segments and angles are congruent 2. To construct flowcharts to illustrate the logical flow of an argument 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 sides are congruent • Corresponding angles are congruent 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 1. AC AB Given AC AB CD BD Prove : CAD BAD Given : 2. CD BD Given 3. AD AD Reflexive Property 4. ACD ABD SSS Postulate 5. CAD BAD CPCTC Investigation 1 In your notebook, 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.