1. Warm Up: Tell whether it is possible to draw each triangle. 1.Acute scalene triangle 2.Obtuse equilateral triangle 3.Right isosceles triangle 4.Scalene equiangular triangle 5.Right scalene triangle

2. 4.3 Congruent Triangles

3. 4.3 – Congruent Triangles Two geometric figures are congruent if they have exactly the same size and shape. When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

4. A B C P Q R Ex 1: Illustrate the two triangles. What angles corresponding to what angles?

5. Ex 2: ABCD is  to HGFE, find x and y. A B DC F E G H 91 o 86 o 9cm (5y-12) o (4x-3)cm 113 o

6. Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

7. Properties of Congruent Triangles Reflexive Property: Every triangle is congruent to itself. Symmetric Property of Congruent Triangles: If ABC =̃ DEF, then DEF =̃ ABC Transitive Property of Congruent Triangles: If ABC =̃ DEF and DEF =̃ JKL, then ABC =̃ JKL.

8. Ex 4: Given: seg RP  seg MN, seg PQ  seg NQ, seg RQ  seg MQ, m  P = 92 o and m  N is 92 o. Prove: ΔRQP  ΔMQN R P Q N M 92 o

9. Section 4.4 Proving Triangles Congruent: SSS and SAS

10. Using the SSS Postulate Side side side postulate: If three sides of one triangle are congruent to three sides of another triangle, the the two triangles are congruent.

11. Example 1 Prove the triangles congruent. A B C D StatementReason 1. 2. 3.

12. Use the SSS Congruence Postulate to show that  ABC   FGH.

13. Using the SAS Postulate Side angle side postulate: If two sides and the included angle of one triangle are congruent to two sided and the included angle of another triangle, then the two triangles are congruent.

14. Example 2 Prove the triangles congruent. AB C D StatementReason 1. 2. 3. 4.

15. Section 4.5 Proving Triangles Congruent: ASA and AAS

16. Using the ASA Postulate Angle side angle postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent.

17. Example 1 Prove the triangles congruent. StatementReason M N O P M N O P N P

18. Using the AAS Theorem Angle angle side theorem: If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of another triangle, then the two triangles are congruent.

19. Example 2 Prove the triangles congruent. StatementsReasons P Q R S T

20. Given: AD ║EC, BD  BC Prove: ∆ABD  ∆EBC StatementsReasons