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Triangle Congruence by SSS and SAS

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. Triangle Congruence by SSS and SAS. GEOMETRY LESSON 4-2.

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Triangle Congruence by SSS and SAS

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  1. 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. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 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 DWODWG? 5. Can you prove SEDBUT from the information given? Explain. N 4-2

  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 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.PRPR6.AD L N By the Reflexive Property of Congruence, a segment is congruent to itself Third Angles Theorem Check Skills You’ll Need 4-3

  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

  4. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3

  5. 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

  6. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3

  7. The diagram shows NAD and FNCAGD. If F C, thenF C G Therefore, FNI CAT GDO by ASA. 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. Quick Check 4-3

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

  9. Because AB || CD, BAC DCA by the Alternate Interior Angles Theorem. Then ABCCDA if a pair of corresponding sides are congruent. By the Reflexive Property, ACAC soABCCDA by AAS. 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 D, AB || CD Prove: ABCCDA Quick Check 4-3

  10. 1. B D, AB || CD1. Given 3. BAC DCA3. Alternate Interior Angle Theorem . 4. ACCA4. Reflexive Property of Congruence 5. ABCCDA5. AAS Theorem 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: ABCCDA Statements Reasons 2. BAC & DCA are AIA 2. Definition of Alternate Interior Angle. Quick Check 4-3

  11. RF GHI PQRAAS ABX ACXAAS 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? 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. 5. S and U not possible 4-3

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