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Happy Monday Do Before the Bell Rings: 1. Pick up the papers from the front table. 2. Have your homework out on your desk with a red pen. 3. Take out your whiteboard and whiteboard pens. Math History Presentations will be due tomorrow! 3 Things Do Now!: Whiteboards 1. Find mABD. 1. ∆PQR ∆STW Name all pairs of congruent corresponding parts. 1. Angles: P S, Q T, R W 2. Sides: PQ ST, QR TW, PR SW Whiteboards 3. Name a congruence statement for the following figure. 4.4: Triangle Congruence: SSS and SAS Learning Objective SWBAT apply SSS and SAS to show triangles are congruent. SWBAT prove triangles are congruent by using SSS and SAS. Math Joke of the Day • What do you call a fierce beast? • A line On Friday… • You proved triangles are congruent by showing that all six pairs of corresponding pairs were congruent. • Today, we are learning a shortcut! 4-4 Triangle Congruence: SSS and SAS There are five ways to prove triangles are congruent: 1. SSS 2. SAS 3. ASA 4. AAS 5. HL Today we are going to discuss SSS and SAS. 4-4 Triangle Congruence: SSS and SAS Side–Side–Side Congruence (SSS) • If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. • We abbreviate Side-Side-Side Congruence as SSS. What is a possible congruent statement for the figures? • Examples • Non-Examples 4-4 Triangle Congruence: SSS and SAS Example 1: (a) Use SSS to explain why ∆ABC ∆DBC. It is given that AC DC and that AB DB. By the Reflexive Property of Congruence, BC BC. Therefore ∆ABC ∆DBC by SSS. With your table group: Whiteboards Example #1 b) Use SSS to explain why ∆ABC ∆CDA. Be ready to share out! 4-4 Triangle Congruence: SSS and SAS Included Angle • An angle formed by two adjacent sides of a polygon. • B is the included angle between sides AB and BC. Whiteboards:CFU 1. What is the included angle between the sides BC and CA? 2. What are the sides of the included angle A? Side-Angle-Side Congruence Side–Angle–Side Congruence (SAS) • If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. What is the possible congruence statement for the figures? Example/ Non-Examples • Example • Non-Example 4-4 Triangle Congruence: SSS and SAS Example 2: (a) Use SAS to explain why ∆XYZ ∆VWZ. It is given that XZ VZ and that YZ WZ. By the Vertical s Theorem. XZY VZW. Therefore ∆XYZ ∆VWZ by SAS. Whiteboards Use SAS to explain why ∆ABC ∆DBC. It is given that BA BD and ABC DBC. By the Reflexive Property of , BC BC. So ∆ABC ∆DBC by SAS. Example 3: 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: 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: ∆ABC ∆CDB Proof: Closure Questions Which postulate, if any, can be used to prove the triangles congruent? In one sentence tell why or why not the triangles are congruent. 1. 2. Begin Homework For the remaining time please begin the homework. p. 245: #1-7 If you get stuck: 1. Talk to your tablemates. 2. If all of your tablemates are confused raise your hand and I will assist you as soon as I can.