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1.In VGB, which sides include B? 2.In STN, which angle is included between NS and TN? 3.Which triangles can you prove congruent? Tell whether you would.

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Presentation on theme: "1.In VGB, which sides include B? 2.In STN, which angle is included between NS and TN? 3.Which triangles can you prove congruent? Tell whether you would."— Presentation transcript:

1 1.In VGB, which sides include B? 2.In STN, which angle is included between NS and TN? 3.Which triangles can you prove congruent? Tell whether you would use the SSS or SAS Postulate. 4.What other information do you need to prove DWO DWG? 5.Can you prove SED BUT from the information given? Explain. N Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 BG and BV APB XPY; SAS If you know DO DG, the triangles are by SSS; if you know DWO DWG, they are by SAS. No; corresponding angles are not between corresponding sides. 4-2

2 In JHK, which side is included between the given pair of angles? 1. J and H2. H and K In NLM, which angle is included between the given pair of sides? 3.LN and LM4.NM and LN Give a reason to justify each statement. 5.PR PR 6. A D (For help, go to Lesson 4-2.) GEOMETRY LESSON 4-3 Triangle Congruence by ASA and AAS 4-3 Check Skills Youll Need L N By the Reflexive Property of Congruence, a segment is congruent to itself Third Angles Theorem

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5 Triangle Congruence by ASA and AAS GEOMETRY LESSON An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

6 Triangle Congruence by ASA and AAS GEOMETRY LESSON

7 Triangle Congruence by ASA and AAS GEOMETRY LESSON You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

8 Triangle Congruence by ASA and AAS GEOMETRY LESSON

9 Suppose that F is congruent to C and I is not congruent to C. Name the triangles that are congruent by the ASA Postulate. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Therefore, FNI CAT GDO by ASA. If F C, then F C G The diagram shows N A D and FN CA GD. 4-3 Quick Check Using ASA

10 Write a paragraph proof. Given: A B, AP BP Prove: APX BPY Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 It is given that A B and AP BP. APX BPY by the Vertical Angles Theorem. Because two pairs of corresponding angles and their included sides are congruent, APX BPY by ASA. 4-3 Quick Check Writing a proof using ASA

11 Write a Plan for Proof that uses AAS. Given: B D, AB || CD Prove: ABC CDA Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 By the Reflexive Property, AC AC so ABC CDA by AAS. Then ABC CDA if a pair of corresponding sides are congruent. Because AB || CD, BAC DCA by the Alternate Interior Angles Theorem. 4-3 Quick Check Planning a Proof using AAS

12 Write a two-column proof that uses AAS. Given: B D, AB || CD Prove: ABC CDA StatementsReasons Triangle Congruence by ASA and AAS GEOMETRY LESSON B D, AB || CD1. Given 5. ABC CDA5. AAS Theorem 3. BAC DCA3. Alternate Interior Angle Theorem AC CA4. Reflexive Property of Congruence Quick Check Writing a proof using AAS 2. BAC & DCA are AIA2. Definition of Alternate Interior Angle.

13 1.Which side is included between R and F in FTR? 2.Which angles in STU include US? 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 RF S and U Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 GHI PQR AAS not possible ABX ACX AAS 4-3


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