2. Triangle Congruency

3. Classifying Triangles by Sides Equilateral Triangle 3 congruent sides Isosceles Triangle At least 2 congruent sides Scalene Triangle No congruent sides

4. Classifying Triangles by Angles Acute Triangle Equiangular Triangle Right Triangle Obtuse Triangle 3 acute angles 3 congruent angles 1 right angle 1 obtuse angle Note: An equiangular triangle is also acute.

5. Terms to remember Vertex Plural: Vertices

6. More terms adjacent sides side opposite  C

7. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°. m  A + m  B + m  C = 180°

8. Term congruent figures – Two geometric figures that have exactly the same size and shape. All pairs of corresponding angles and sides are congruent. symbol: 

9. Example 1  A   F,  C   D,  B   E AB  FE, BC  ED, CA  DF ∆ABC  ∆ FED Identify all pairs of congruent corresponding parts and write a congruence statement

10. Example 3 Find the value of x. (2x+30)° m  M = 180º - 55º - 65 º m  M = 60 º m  M = m  T 60 = 2x + 30 x = 15

11. Try This! Find the value of x. (4x+15)°

12. Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

13. Example 1 StatementsReasons

14. Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

15. Example 2 Prove: ∆AEB  ∆CED StatementsReasons

16. 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. If  A   D, AC  DF, and  C   F, then  ABC   DEF

17. Angle-Angle-Side (AAS) Congruence Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent. If  A   D,  C   F, and BC  EF, then  ABC   DEF

18. Hypotenuse-Leg (HL) Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

19. Example 2 Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Yes! AASNo!

20. 1 2 3 4 Try This! Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Yes! ASA No! AAA is NOT a congruence postulate or theorem

21. Homework Page 238 numbers 1-3, 13,14 Page 244 numbers 2, 4, 10, 12, 14, 15 Page 251 Numbers 2-14 Evens