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Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 1. In VGB, which sides include B? BG and BV 2. In STN, which angle is included between NS and TN? N 3. Which triangles can you prove congruent? Tell whether you would use the SSS or SAS Postulate. APB XPY; SAS 4. What other information do you need to prove DWO DWG? If you know DO DG, the triangles are by SSS; if you know DWO DWG, they are by SAS. 5. Can you prove SED BUT from the information given? Explain. No; corresponding angles are not between corresponding sides. 4-2 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 (For help, go to Lesson 4-2.) In JHK, which side is included between the given pair of angles? 1. J and H 2. H and K HK JH In NLM, which angle is included between the given pair of sides? 3. LN and LM 4. NM and LN L N Give a reason to justify each statement. 5. PR PR 6. A By the Reflexive Property of Congruence, a segment is congruent to itself D Third Angles Theorem Check Skills You’ll Need 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side. 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS). 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Using ASA Suppose that F is congruent to C and I is not congruent to C. Name the triangles that are congruent by the ASA Postulate. The diagram shows N If F C, then F Therefore, FNI A C CAT D and FN CA GD. G GDO by ASA. Quick Check 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Writing a proof using ASA Write a paragraph proof. Given: A Prove: B, AP APX It is given that A APX BP BPY B and AP BP. BPY by the Vertical Angles Theorem. Because two pairs of corresponding angles and their included sides are congruent, APX BPY by ASA. Quick Check 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Planning a Proof using AAS Write a Plan for Proof that uses AAS. Given: B Prove: D, AB || CD ABC CDA Because AB || CD, BAC Interior Angles Theorem. DCA by the Alternate Then ABC CDA if a pair of corresponding sides are congruent. By the Reflexive Property, AC ABC CDA by AAS. AC so Quick Check 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Writing a proof using AAS Write a two-column proof that uses AAS. Given: B D, AB || CD Prove: ABC CDA Statements Reasons 1. B 1. Given D, AB || CD 2. BAC & DCA are AIA 2. Definition of Alternate Interior Angle. 3. BAC DCA 3. Alternate Interior Angle Theorem . 4. AC 5. CA ABC 4. Reflexive Property of Congruence CDA 5. AAS Theorem Quick Check 4-3 Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 1. Which side is included between R and F in FTR? 2. Which angles in STU include US? S and U RF Tell whether you can prove the triangles congruent by ASA or AAS. If you can, state a triangle congruence and the postulate or theorem you used. If not, write not possible. 3. 4. GHI AAS PQR 5. not possible 4-3 ABX AAS ACX