2. 4.10 Prove Triangles Cong. by ASA and AAS 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. A C B D E F

3. 4.10 Prove Triangles Cong. by ASA and AAS 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. A C B D E F

4. 4.10 Prove Triangles Cong. by ASA and AAS Theorem 4.14: Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pair of alternate interior angles are _________. congruent 4 5 p q t

5. 4.10 Prove Triangles Cong. by ASA and AAS 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. a. a.There is not enough information to prove the triangles congruent, because no _______ are known to be the congruent. sides

6. 4.10 Prove Triangles Cong. by ASA and AAS 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. b. b.Two pairs of angles and a ______________ pair of sides are congruent. The triangles are congruent by the _____________________________. non-included AAS Congruence Theorem

7. so two pairs of angles and their _______________ are congruent. The triangles are congruent by the ____________________________. 4.10 Prove Triangles Cong. by ASA and AAS 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. c. c.The vertical angles are congruent, included sides ASA Congruence Postulate

8. 4.10 Prove Triangles Cong. by ASA and AAS Checkpoint. Complete the following exercises. 1.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 T U W V you have two pairs of angles and a non-included pair of sides. The triangles are congruent by the AAS Congruence Theorem

9. 4.10 Prove Triangles Cong. by ASA and AAS Example 2 Write a flow proof In the diagram, 1 4 and CF bisects ACE. Write a flow proof to show CBF CDF. C E B A D F 1 2 3 4 Given: Prove: Given Def. of _______________ angles supplements supplementary Cong. Supps. Thm. Reflexive Prop. _________________________ AAS Congruence Theorem

10. 4.10 Prove Triangles Cong. by ASA and AAS Checkpoint. Complete the following exercises. C E B A D F 1 2 3 4 2.In the diagram, CF bisects ACE and BFD. Write a flow proof to show CBF CDF. Given: Prove: Given Def. of bisector Reflexive Prop. ASA Congruence Postulate

11. 4.10 Prove Triangles Cong. by ASA and AAS Pg. 267, 4.10 #1-20