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4.4 SSS and SAS2 ink.notebook November 08, 2016 page 158 page 157 page 156 4.4 SSS and SAS Lesson Objectives Standards Lesson Notes page 159 4.4 SSS and SAS Press the tabs to view details. 1 4.4 SSS and SAS2 ink.notebook Lesson Objectives Standards November 08, 2016 Lesson Notes Standards Lesson Objectives After this lesson, you should be able to successfully use SSS and SAS to prove triangles are congruent. Lesson Notes G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Press the tabs to view details. G.CO.10 Prove theorems about triangles. SIDESIDESIDE (SSS) CONGRUENCE POSTULATE You know that two triangles are congruent if corresponding sides are congruent and corresponding angles are congruent. The following postulates lets you show that two triangles are congruent if you know only about congruent sides and angles in a specific order. If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. C B A S R T 2 4.4 SSS and SAS2 ink.notebook November 08, 2016 Decide whether the congruence statement is true. Explain your reasoning. a) ÆJKL ¤ ÆMKL L 9 9 8 8 J K b) ÆRST ¤ ÆTVW W R M S T V 3 4.4 SSS and SAS2 ink.notebook November 08, 2016 B c) Finish the twocolumn proof Given: AB ¤ DB and C is the midpoint of AD Prove: ÆABC ¤ ÆDBC A Statements C D Reasons 1. AB ¤ DB 1. 2. C is the midpoint of AD 2. 3. AC ¤ DC 3. Defn of _____________ 4. BC ¤ BC 4. 5. ÆABC ¤ ÆDBC 5. SIDEANGLESIDE (SAS) CONGRUENCE POSTULATE If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. S R V T U W 4 4.4 SSS and SAS2 ink.notebook November 08, 2016 For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate. e) d) è______ ¤ è _____ è______ ¤ è _____ by the _____ Postulate. by the _____ Postulate. f) The included angles, Ú1 and Ú2, are congruent because _________________________________. è______ ¤ è _____ by the _____ Postulate. In ΔABC, the angle is not "included" by the sides So the triangles cannot be proved congruent by the SAS Postulate. THERE IS NO “DONKEY” (AS–S or SSA) Theorem! A B D C E F 5 4.4 SSS and SAS2 ink.notebook November 08, 2016 g) Finish the twocolumn proof L J 1 Given: JN ¤ LN, KN ¤ MN Prove: ÆJKN ¤ ÆLMN N 2 M K Statements 1. JN ¤ ____ Reasons 1. KN ¤ ____ 2. Ú1 ¤ Ú2 3. ÆJKN ¤ ÆLMN 2. 3. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, write not possible. On the Worksheet 1. 2. 3. 6 4.4 SSS and SAS2 ink.notebook November 08, 2016 Determine whether ΔABC ¤ ΔKLM. Explain. Determine whether ΔABC ¤ ΔKLM. Explain. 5. A( 4, 2), B(–4, 1), C(–1, –1), K(0, –2), L(0, 1), M(4, 1) – 4. A(–3, 3), B(–1, 3), C(–3, 1), K(1, 4), L(3, 4), M(1, 6) y – y x x 6. INDIRECT MEASUREMENT To measure the width of a sinkhole on his property, Harmon marked off congruent triangles as shown in the diagram. How does he know that the lengths A′B′ and AB are equal? Practice 7 4.4 SSS and SAS2 ink.notebook November 08, 2016 8 4.4 SSS and SAS2 ink.notebook November 08, 2016 9 4.4 SSS and SAS2 ink.notebook November 08, 2016 Answers: BOOKWORK Answers page 2: 1. SSS 3. None 5. SSS 7. SAS 9. SSS 11. SAS Answers page 3: first proof: Given, SAS In the book, do page 267 – 269, problems: 8, 9, 16 – 19, 35 10 4.4 SSS and SAS2 ink.notebook November 08, 2016 y x 11