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Happy Tuesday Do Before the Bell Rings: 1. Pick up the paper from the front table 2. Take out notes from yesterday 3. Have your homework out on your desk with a red pen. 4. Take out your whiteboard and whiteboard pens. Math History Presentations will be TODAY! Math History Presentations Warm Up: Whiteboards 1. What are sides AC and BC called? Side AB? legs; hypotenuse 2. Which side is in between A and C? 3. Given DEF and GHI, if D G and E H, why is F I? Third s Thm. Example from yesterday: Verifying Triangle Congruence Show that the triangles are congruent for the given value of the variable. ∆MNO ∆PQR, when x = 5. PQ MN, QR NO, PR MO ∆MNO ∆PQR by SSS. Whiteboards Show that the triangles are congruent for the given value of the variable. ∆STU ∆VWX, when y = 4. ST VW, TU WX, and T W. ∆STU ∆VWX by SAS. 4-4 Triangle Congruence: SSS and SAS Example 3 ( from yesterday): The Hatfield and McCoy families are feuding over some land. Neither family will be satisfied unless the two triangular fields are exactly the same size. You know that BC is parallel to AD and the midpoint of each of the intersecting segments. Write a two-column proof that will settle the dispute. . Given: BC || AD, BC AD Prove: ∆ABD ∆CDB Proof: 4.5: Triangle Congruence: ASA, AAS, and HL Learning Objective SWBAT prove triangles congruent by using ASA, AAS, and HL. Math Joke of the Day • What do you call a broken angle? • A rectangle! 4.5 Triangle Congruence: SSS and SAS There are five ways to prove triangles are congruent: 1. SSS yesterday 2. SAS 3. ASA Today! 4. AAS 5. HL Included Side • Yesterday we learned what an included angle is. What do you think an included side would be? Included side • common side of two consecutive angles in a polygon. 4-4 Triangle Congruence: SSS and SAS Angle–Side–Angle Congruence (ASA) • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent • . What is a possible congruent statement for the figures? ASA • Examples • Non-Examples Example 1 Example 1: (a) Use ASA to explain why ∆UXV ∆WXV. Whiteboard Determine if you can use ASA to prove NKL LMN. Explain. By the Alternate Interior Angles Theorem. KLN MNL. NL LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied. Angle-Angle-Side Congruence Angle-Angle-Side(AAS) • If two angles and a non-included side of one triangle are congruent to the corresponding angles and a side of a second triangle, then the two triangles are congruent. What is the possible congruence statement for the figures? Example/ Non-Examples: AAS • Example • Non-Example Proof of AAS Example 2: Example 3 Use AAS to prove the triangles congruent. Given: JL bisects KLM, K M Prove: JKL JML Hypotenuse-Leg (HL) Congruence Hypotenuse-Leg Congruence (HL) • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. Examples/Non-Examples: HL • Example • Non-Example Example 4 Prove ABC DCB. Yes; it is given that AC DB. BC CB by the Reflexive Property of Congruence. Since ABC and DCB are right angles, ABC and DCB are right triangles. ABC DCB by HL. Whiteboards Identify the postulate or theorem that proves the triangles congruent. HL ASA SAS or SSS Homework • Worksheet online! – The answers are on the bottom but try it yourself first – I will not be here tomorrow