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4.10

4.10. Prove Triangles Cong. by ASA and AAS. E. B. F. D. C. A. Angle-Side-Angle (ASA) Congruence Postulate. If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. 4.10.

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4.10

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  1. 4.10 Prove Triangles Cong. by ASA and AAS E B F D C A Angle-Side-Angle (ASA) Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

  2. 4.10 Prove Triangles Cong. by ASA and AAS E B F D C A Theorem 4.13: Angle-Angle-Side (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. 4.10 Prove Triangles Cong. by ASA and AAS t p q Theorem 4.14: Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pair of alternate interior angles are _________. 4 congruent 5

  4. 4.10 Prove Triangles Cong. by ASA and AAS Identify congruent triangles Example 1 Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. a. • There is not enough information to prove the triangles congruent, because no _______ are known to be the congruent. sides

  5. 4.10 Prove Triangles Cong. by ASA and AAS Identify congruent triangles Example 1 Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. b. non-included • Two pairs of angles and a ______________ pair of sides are congruent. The triangles are congruent by the _____________________________. AAS Congruence Theorem

  6. 4.10 Prove Triangles Cong. by ASA and AAS Identify congruent triangles Example 1 Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. c. • The vertical angles are congruent, so two pairs of angles and their _______________ are congruent. The triangles are congruent by the ____________________________. included sides ASA Congruence Postulate

  7. 4.10 Prove Triangles Cong. by ASA and AAS • Can STW and VWT be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. S V U T W Checkpoint. Complete the following exercises. you have two pairs of angles and a non-included pair of sides. The triangles are congruent by the AAS Congruence Theorem

  8. 4.10 Prove Triangles Cong. by ASA and AAS In the diagram, 1 4 and CF bisects ACE. Write a flow proof to show CBF CDF. C D B 2 3 1 4 E A F Def. of _______________ angles Cong. Supps. Thm. _________________________ Write a flow proof Example 2 Given: Prove: supplements supplements Given supplementary Given Reflexive Prop. AAS Congruence Theorem

  9. 4.10 Prove Triangles Cong. by ASA and AAS C • In the diagram, CF bisects ACE and BFD. Write a flow proof to show CBF CDF. D B 2 3 1 4 E A F Def. of bisector Def. of bisector Checkpoint. Complete the following exercises. Given: Prove: Given Given Reflexive Prop. ASA Congruence Postulate

  10. 4.10 Prove Triangles Cong. by ASA and AAS Pg. 267, 4.10 #1-20

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