# provingtrianglescongruentssssasasa-091123170916-phpapp01.ppt

24 de May de 2023                               1 de 31

### provingtrianglescongruentssssasasa-091123170916-phpapp01.ppt

• 2. The Idea of a Congruence Two geometric figures with exactly the same size and shape. F B A C E D
• 3. Congruent figures can be rotations of one another.
• 4. Congruent figures can be reflections of one another.
• 5. How much do you need to know. . . . . . about two triangles to prove that they are congruent?
• 6. Corresponding Parts We learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
• 7.  In proving the congruency of two triangles, we do not need all the six corresponding parts but only 3 parts. Either the three sides, two sides and one angle or two angles and one side.
• 8. Side-Side-Side (SSS) Two triangles are congruent if all the three sides of one triangle are equal to the three sides of other triangle.
• 9. Side-Angle-Side (SAS) • AB ≅ DE • ∠A ≅ ∠D • AC ≅ DF ∆ABC ≅ ∆DEF included angle Two triangles are congruent if any two sides and the includes angle of triangle is equal to the two sides and the included angle of other triangle.
• 10. Included Angle The angle between two sides
• 11. Included Angle Name the included angle: YE and ES ES and SY SY and YE
• 12. Angle-Side-Angle (ASA) • ∠ A ≅ ∠ D • ∠ B ≅ ∠ E • BC ≅ EF ∆ABC ≅ ∆ DEF Included Side Two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
• 13. Included Side The side between two angles GI HI GH
• 14. E Y S Included Side Name the included side: ZY and ZE YE ZE and ZS ES ZS and ZY SY
• 15. Angle-Angle-Side (AAS) • ∠ A ≅ ∠ D • ∠ B ≅ ∠ E • BC ≅ EF ∆ABC ≅ ∆DEF Non-included side Two triangles are congruent if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle.
• 16. Warning: No SSA Postulate B E NOT CONGRUENT F There is no such thing as an SSA postulate!
• 17. Warning: No AAA Postulate NOT CONGRUENT B E There is no such thing as an AAA postulate! A C D F
• 18. The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence ndence dence
• 19. NAME THE POSTULATE
• 21. Name That Postulate (when possible) Reflexive Property Vertical Angles Vertical Angles Reflexive Property
• 22. I. Let’s Practice Name That Postulate 1. 4. 3. 2.
• 23. 5. 6. 7.
• 24. II. Let’s Practice 1. Indicate the additional information needed to enable us to apply the specified congruence postulate.
• 25. 2. Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
• 26. 3. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. G K
• 27. 4. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. B A C E
• 28. 5. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. C B A E D
• 29. 6. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
• 30. 7. Determine if whether each pair of triangles are congruent by SSS, SAS, ASA, or AAS. If not possible to prove that they are congruent, write notpossible. J L T