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Concept
Write a two-column proof. Use ASA to Prove Triangles Congruent Write a two-column proof. Example 1
4. Alternate Interior Angles Use ASA to Prove Triangles Congruent Proof: Statements Reasons 1. Given 1. L is the midpoint of WE. ____ 2. 2. Midpoint Theorem 3. 3. Given 4. W E 4. Alternate Interior Angles 5. WLR ELD 5. Vertical Angles Theorem 6. ΔWRL ΔEDL 6. ASA Example 1
Concept
Write a paragraph proof. Use AAS to Prove Triangles Congruent Write a paragraph proof. Example 2
Apply Triangle Congruence MANUFACTURING Barbara designs a paper template for a certain envelope. She designs the top and bottom flaps to be isosceles triangles that have congruent bases and base angles. If EV = 8 cm and the height of the isosceles triangle is 3 cm, find PO. Example 3
Concept
Proving RIGHT TRIANGLES congruent *As long as statement(s) mention right angles, you only need 2 congruent pieces in each triangle: each hypotenuse and corresponding legs. Hence, HL. Concept
Example 4: Determine whether each pair of triangles is congruent. If yes, state the postulate/theorem that applies. 4. 5. 6. Each triangle has right angles that are congruent, a 2nd set of corresponding angles that are congruent, and a side in between the 2 angles that is congruent. ASA Each triangle has right angles that are congruent, a 2nd set of corresponding angles that are congruent, and a 3rd set of corresponding angles that are congruent. NOT POSSIBLE. (AAA does not exist) Each triangle has right angles that are congruent, a set of corresponding sides that are congruent, and share a side, but SSA does not exist. (the angle is not the included angle). However, because the triangles are right triangles, they share the hypotenuse, and have a set of congruent legs. HL Concept
Given: AB BC, DC BC, AC BD Example 5: Complete the proof. Given: AB BC, DC BC, AC BD Prove: ΔABC ΔDCB Proof: Reasons Statements 1. 2. 3. Given 4. Definition of 5. 6. Reflexive Property 7. Given Definition of DCB is a right angle Given HL ΔABC ΔDCB Concept
End of the Lesson
Five-Minute Check (over Lesson 4–4) CCSS Then/Now New Vocabulary Postulate 4.3: Angle-Side-Angle (ASA) Congruence Example 1: Use ASA to Prove Triangles Congruent Theorem 4.5: Angle-Angle-Side (AAS) Congruence Example 2: Use AAS to Prove Triangles Congruent Example 3: Real-World Example: Apply Triangle Congruence Concept Summary: Proving Triangles Congruent Lesson Menu
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSS B. ASA C. SAS D. not possible 5-Minute Check 1
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSS B. ASA C. SAS D. not possible 5-Minute Check 2
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SAS B. AAS C. SSS D. not possible 5-Minute Check 3
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSA B. ASA C. SSS D. not possible 5-Minute Check 4
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. AAA B. SAS C. SSS D. not possible 5-Minute Check 5
Given A R, what sides must you know to be congruent to prove ΔABC ΔRST by SAS? 5-Minute Check 6
G.CO.10 Prove theorems about triangles. Content Standards G.CO.10 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 5 Use appropriate tools strategically. CCSS
You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence. Use the AAS Theorem to test for congruence. Then/Now
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