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Prove Triangles Congruent by ASA & AAS

Prove Triangles Congruent by ASA & AAS. Lesson 4.10 Use two more methods to prove congruences. Vocabulary. A flow proof uses arrows to show the flow of a logical argument.

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Prove Triangles Congruent by ASA & AAS

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  1. Prove Triangles Congruent by ASA & AAS Lesson 4.10 Use two more methods to prove congruences

  2. Vocabulary • A flow proof uses arrows to show the flow of a logical argument. • ASA Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles & included side of a second triangle, then the two triangles are congruent • AAS Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

  3. Triangle Congruence Review Postulates we can use CAN’T USE

  4. Tell whether the pair of triangles is congruent or not and why. Yes; HL Thm. ANSWER Lesson 4.5, For use with pages 249-255

  5. The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem. EXAMPLE 1 Identify congruent triangles Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.

  6. There is not enough information to prove the triangles are congruent, because no sides are known to be congruent. Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate. EXAMPLE 1 Identify congruent triangles

  7. C F, BC EF A D, GIVEN ABCDEF PROVE EXAMPLE 2 Prove the AAS Congruence Theorem Prove the Angle-Angle-Side Congruence Theorem. Write a proof.

  8. ASA Congruence Postulate

  9. AAS Congruence Theorem

  10. RSTVUT RSTVUT STATEMENTS REASONS Given S U Given RS UV The vertical angles are congruent RTSUTV for Examples 1 and 2 GUIDED PRACTICE In the diagram at the right, what postulate or theorem can you use to prove that ? Explain. SOLUTION AAS

  11. ABC GIVEN m 1 + m 2 + m 3 = 180° PROVE STATEMENTS REASONS Rewrite the proof of the Triangle Sum Theorem on page219as a flow proof. 1. Parallel Postulate 1. Draw BDparallel to AC. 2. m 4 + m 2 + m 5 2. = 180° Angle Addition Postulate and definition of straight angle , 4 3. 1 5 3. 3 Alternate Interior Angles Theorem m 4 m 5 4. m 1 = , m 3 = 4. Definition of congruent angles 5. m 1 + m 2 + m 3 5. Substitution Property of Equality = 180° for Examples 1 and 2 GUIDED PRACTICE

  12. GIVEN CE BD, ∠ CAB CAD ABEADE PROVE EXAMPLE 3 Write a flow proof In the diagram,CE BDand∠ CAB CAD. ABEADE Write a flow proof to show

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