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Unit 4: Triangle Congruence 4.5 Triangle Congruence: ASA 4.5 Triangle Congruence: ASA Warm Up 12/01/11 (HW #23 [4.5] Pgs 257 - 258 #s 11, 12, 14 – 17, 22) 1. Show that ∆ADB ∆CDB, t = 4. 4.5 Triangle Congruence: ASA Warm Up 12/01/11 (HW #23 [4.5] Pgs 257 - 258 #s 11, 12, 14 – 17, 22) 1. What are sides AC and BC called? Side AB? 2. Which side is in between A and C? 3. Given DEF and GHI, if D G and E H, why is F I? Objectives (see page 252) Apply ASA to construct triangles and to solve problems. Prove triangles congruent by using ASA. *Standard 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. *also Standard 4.0 Students prove basic theorems involving congruence and similarity. *also Standard 2.0 Students write geometric proofs, including proofs by contradiction. *see page 252 An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side. Your Goal! Discuss and Decide if you can… create 2 triangles that are exactly the same Your task (how you will accomplish your goal)! 1. Find your partner who has the same size and color marked bamboo stick OR angle as you 2. With your partner, form a group of 6 (you should have 2 bamboo sticks and 4 angles) 3. Within your group of 6, can you form 2 triangles that are the same using 2 angles and an included side (bamboo stick) for each? (on the paper provided, write your response and a figure or words to describe how you know) Your Goal! Discuss and Decide if you can… create 2 triangles that are exactly the same Your task (continued)! 4. Now that you’ve discussed and decided that each group has 2 exactly the same triangles… set aside one triangle and focus on the other triangle. Keeping the 2 angles with the included side together, can you rearrange the triangle to make it different from the triangle you set aside? *see page 252 Example 2: Applying ASA Congruence page 253) (see example 2 on Determine if you can use ASA to prove the triangles congruent. Explain. Check It Out! Example 2 (see page 253) Determine if you can use ASA to prove NKL LMN. Explain. Given: FAB GED, ABC DCE, AC EC Prove: ABC EDC Statements Reasons 1. FAB GED 1. 2. BAC is a supp. of FAB; DEC is a supp. of GED. 2. Def. of supp. s 3. BAC DEC 3. Supp. Thm. 4. ACB DCE; AC EC 4. 5. ABC EDC 5.