Unit 4: Triangle Congruence 4.4 Triangle Congruence: SAS

Warm Up 11/30/11 (HW #22 [4.4] Pgs #s 8, 9, 11 – 17) 1. Use SSS to explain why ∆ABC  ∆CDA. 2. Show that the triangles are congruent for the given value of the variable; ∆MNO  ∆PQR, when x = 5  4.4 Triangle Congruence: SAS *for Period 3/5

Warm Up 11/30/11 (HW #22 [4.4] Pgs #s 8, 9, 11 – 17) 1. Show that the triangles are congruent for the given value of the variable. ∆GHJ  ∆IHJ, for x = 4.  4.4 Triangle Congruence: SAS *for Periods 1/6 & 4/7 G H I J 3 5 3x – 9 2x – 3

Apply SAS to construct triangles and solve problems. Prove triangles congruent by using SAS. Objectives (see page 242) *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 2.0 Students write geometric proofs, including proofs by contradiction.

An included angle is an angle formed by two adjacent sides of a polygon.  B is the included angle between sides AB and BC. ~It can also be shown that only two pairs of congruent corresponding sides are needed to prove the congruence of two triangles if the included angles are also congruent.

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 4 bamboo sticks and 2 angles) 3.Within your group of 6, can you form 2 triangles that are the same using 2 bamboo sticks and an included angle 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 sides with the included angle together, can you rearrange the triangle to make it different from the triangle you set aside? Your Goal! Discuss and Decide if you can… create 2 triangles that are exactly the same

The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides. Caution

Example 2: Engineering Application (see page 243) The diagram shows part of the support structure for a tower. Use SAS to explain why ∆ XYZ  ∆ VWZ.

Check It Out! Example 2 (see page 243) Use SAS to explain why ∆ ABC  ∆ DBC.

Check It Out! Example 3 (see page 244) Show that ∆ADB  ∆CDB, t = 4.

Example 3B: Verifying Triangle Congruence (see pg 244) ∆STU  ∆VWX, when y = 4. Show that the triangles are congruent for the given value of the variable.

Example 4: Proving Triangles Congruent (see pg 244) Given: BC || AD, BC  AD Prove: ∆ABD  ∆CDB ReasonsStatements 5. ∆ ABD  ∆ CDB 3. Given 2. Alt. Int.  s Thm.2.  CBD   ABD 1. Given1. BC || AD 4. BD  BD

Check It Out! Example 4 (see pg 244) Given: QP bisects  RQS. QR  QS Prove: ∆RQP  ∆SQP ReasonsStatements ∆ RQP  ∆ SQP Given  RQP   SQP QP bisects  RQS 1. QR  QS 4. QP  QP