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Prove Triangles Congruent by ASA & AAS

Prove Triangles Congruent by ASA & AAS. Lesson 4.10 (M1) Use two more methods to prove triangle congruence. 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 (M1) Use two more methods to prove triangle congruence

  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 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. ASA Congruence Postulate

  4. AAS Congruence Theorem

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

  6. RTSUTV for Examples 1 and 2 GUIDED PRACTICE ANSWER Therefore are congruent because vertical angles are congruent so two pairs of angles and a pair of non included side are congruent. The triangle are congruent by AAS Congruence Theorem.

  7. ABC GIVEN m 1 + m 2 + m 3 = 180° PROVE STATEMENTS REASONS 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

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