1. Conditions for Triangles Congruence

2. The Idea of a Congruence Two geometric figures with exactly the same size and shape. F BACEDConditions for Triangle Congruence 3. How much do you need to know. . .. . . about two triangles to prove that they are congruent? Conditions for Triangle Congruence 4. Corresponding Parts In the previous lesson, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. 1. AB DE 2. BC EF3. AC DF 4. A DABC DEF5. B E 6. C FConditions for Triangle Congruence 5. QUESTION!Do you need all six ?NO !Conditions for Triangle Congruence 6. The Conditions for Triangle Congruence SSS SAS ASA SAASide, Side, Side Congruence Postulate Side, Angle, Side Congruence Postulate Angle, Side, Angle Congruence Postulate Side, Angle, Angle Congruence TheoremWoohooConditions for Triangle Congruence 7. Side-Side-Side (SSS) Corresponding Sides are Congruent1. AB DE2. BC EFABC DEF3. AC DF Conditions for Triangle Congruence 8. Side-Angle-Side (SAS)1. AB DE 2. A DABC DEF3. AC DF included angleTwo corresponding sides and corresponding included angles are congruent 9. Included Angle The angle between two sidesGIHConditions for Triangle Congruence 10. Included Angle Name the included angle: EYE and ESES and YS YSE SYS and YEYConditions for Triangle Congruence 11. Angle-Side-Angle (ASA)1. A D 2. AB DEABC DEF3. B E included sideTwo corresponding angles and corresponding included sides are congruent 12. Included Side The side between two anglesGIHIGHConditions for Triangle Congruence 13. Included Side Name the included side: EY and E E and S YSYEESS and YSYConditions for Triangle Congruence 14. Side-Angle-Angle (SAA)1. A D 2. B EABC DEF3. BC EF Two corresponding angles and corresponding non-included sides are congruentNon-included side 15. Warning: No SSA Postulate There is no such thing as an SSA postulate! EBF ACDNOT CONGRUENT Conditions for Triangle Congruence 16. Warning: No AAA Postulate There is no such thing as an AAA postulate! EBACDFNOT CONGRUENT Conditions for Triangle Congruence 17. Check your understanding Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruentSASSSA not congruentASASSS 18. Check your understanding Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruentAAA not congruentSASASAnot congruentSSA 19. Check your understanding Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruentReflexive PropertySASVertical AnglesSASVertical AnglesSASReflexive PropertySSAnot congruent 20. Seatwork Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruent(3)(1)(2) (4) 21. Seatwork Name that Condition! If the triangles are congruent, identify the condition that justifies the congruence. If not, state that they are not congruent(6)(5)(7) 22. Lets Practice Indicate the additional information needed to enable to apply the specified congruence postulate. For ASA:B DFor SAS:AC FEFor SAA:A F 23. Check your understanding Indicate the additional information needed to enabble to apply the specified congruence postulate. For ASA:For SAS: For SAA: 24. Conditions for Triangle Congruence 25. The Congruence Conditions SSS congruence ASA congruence SAS congruence SAA congruence SSA congruence AAAcongruence Conditions for Triangle Congruence 26. Thank Thank you! you! 27. Acknowledgement This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching. Revisions made by Mr. Gilbert Joseph Abueg, February 18, 2014