1. Proving Congruent Triangles: SSS & SAS Ch 4 Lesson 3

2. Two Triangles Are Congruent Have to prove 6 parts of the triangle are congruent –Congruent Side (3 sides) –Congruent Angles (3 angles)

3. Postulate 19: Side-Side-Side, SSS If three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent. Side AB ≅ DE Side BC ≅ EF Side CA ≅ FD  Δ ABC ≅ Δ DEF

4. Postulate 19: Side-Side-Side, SSS If three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent. Side AB ≅ DE Side BC ≅ EF Side CA ≅ FD  Δ ABC ≅ Δ DEF

5. Postulate 19: Side-Side-Side, SSS If three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent. Side AB ≅ DE Side BC ≅ EF Side CA ≅ FD  Δ ABC ≅ Δ DEF

6. Postulate 19: Side-Side-Side, SSS If three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent. Side AB ≅ DE Side BC ≅ EF Side AC ≅ DF  Δ ABC ≅ Δ DEF

7. Postulate 19: Side-Side-Side, SSS If three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent. Side AB ≅ DE Side BC ≅ EF Side CA ≅ FD  Δ ABC ≅ Δ DEF

8. Postulate 20: Side-Angle-Side, SAS If two sides and the angle between those two sides are congruent to the two sides and the angle between the two sides of another angle  the two triangles are congruent. Side AB ≅ DE Angle <A ≅ <D Side AC ≅ DF

9. Postulate 20: Side-Angle-Side, SAS If two sides and the angle between those two sides are congruent to the two sides and the angle between the two sides of another angle  the two triangles are congruent. Side AB ≅ DE Angle <A ≅ <D Side AC ≅ DF

10. Postulate 20: Side-Angle-Side, SAS If two sides and the angle between those two sides are congruent to the two sides and the angle between the two sides of another angle  the two triangles are congruent. Side AB ≅ DE Angle <A ≅ <D Side AC ≅ DF

11. Postulate 20: Side-Angle-Side, SAS If two sides and the angle between those two sides are congruent to the two sides and the angle between the two sides of another angle  the two triangles are congruent. Side AB ≅ DE Angle <A ≅ <D Side AC ≅ DF  Δ ABC ≅ Δ DEF

12. Postulate 20: Side-Angle-Side, SAS If two sides and the angle between those two sides are congruent to the two sides and the angle between the two sides of another angle  the two triangles are congruent. Side AB ≅ DE Angle <A ≅ <D Side AC ≅ DF  Δ ABC ≅ Δ DEF

13. Example #1 Prove that Δ ABC ≅ Δ DEF Given BE ≅ EC and AE ≅ ED Set up two column proof

14. Prove that Δ ABC ≅ Δ DEF Statement BE ≅ EC and AE ≅ ED <1 ≅ <2 Δ ABC ≅ Δ DEF Reason Given Vertical Angles SAS congruent postulate

15. Prove that Δ ABC ≅ Δ DEF Statement BE ≅ EC and AE ≅ ED <1 ≅ <2 Δ ABC ≅ Δ DEF Reason Given Vertical Angles SAS congruent postulate

16. Prove that Δ ABC ≅ Δ DEF Statement BE ≅ EC and AE ≅ ED <1 ≅ <2 Δ ABC ≅ Δ DEF Reason Given Vertical Angles SAS congruent postulate

17. Prove that Δ ABC ≅ Δ DEF Statement BE ≅ EC and AE ≅ ED <1 ≅ <2 Δ ABC ≅ Δ DEF Reason Given Vertical Angles SAS congruent postulate

18. Example #2 Decide whether the two triangles are congruent Given QP ≅ PS Given QR ≅ SR Set up two column proof

19. Decide whether the two triangles are congruent Statement QP ≅ PS QR ≅ SR PR ≅ PR ΔQPR ≅ ΔSPR Reason Given Reflexive property SSS congruent postulate

20. Decide whether the two triangles are congruent Statement QP ≅ PS QR ≅ SR PR ≅ PR ΔQPR ≅ ΔSPR Reason Given Reflexive property SSS congruent postulate

21. Decide whether the two triangles are congruent Statement QP ≅ PS QR ≅ SR PR ≅ PR ΔQPR ≅ ΔSPR Reason Given Reflexive property SSS congruent postulate

22. Decide whether the two triangles are congruent Statement QP ≅ PS QR ≅ SR PR ≅ PR ΔQPR ≅ ΔSPR Reason Given Reflexive property SSS congruent postulate

23. Example #3 Given DR ⊥ AG and AR ≅ RG Prove ΔARD ≅ ΔGRD Set up two column proof

24. Prove ΔARD ≅ ΔGRD Statement DR ⊥ AG <DRA=90°&<DRG =90° <DRA ≅ <DRG AR ≅ RG DR ≅ DR ΔARD ≅ ΔGRD Reason Given Def of ⊥ lines Right Angle congruent th. Given Reflexive Prop. SAS congruent Pos.

25. Prove ΔARD ≅ ΔGRD Statement DR ⊥ AG <DRA=90°&<DRG =90° <DRA ≅ <DRG AR ≅ RG DR ≅ DR ΔARD ≅ ΔGRD Reason Given Def of ⊥ lines Right Angle congruent th. Given Reflexive Prop. SAS congruent Pos.

26. Prove ΔARD ≅ ΔGRD Statement DR ⊥ AG <DRA=90°&<DRG =90° <DRA ≅ <DRG AR ≅ RG DR ≅ DR ΔARD ≅ ΔGRD Reason Given Def of ⊥ lines Right Angle congruent th. Given Reflexive Prop. SAS congruent Pos.

27. Prove ΔARD ≅ ΔGRD Statement DR ⊥ AG <DRA=90°&<DRG =90° <DRA ≅ <DRG AR ≅ RG DR ≅ DR ΔARD ≅ ΔGRD Reason Given Def of ⊥ lines Right Angle congruent th. Given Reflexive Prop. SAS congruent Pos.

28. Prove ΔARD ≅ ΔGRD Statement DR ⊥ AG <DRA=90°&<DRG =90° <DRA ≅ <DRG AR ≅ RG DR ≅ DR ΔARD ≅ ΔGRD Reason Given Def of ⊥ lines Right Angle congruent th. Given Reflexive Prop. SAS congruent Pos.

29. Prove ΔARD ≅ ΔGRD Statement DR ⊥ AG <DRA=90°&<DRG =90° <DRA ≅ <DRG AR ≅ RG DR ≅ DR ΔARD ≅ ΔGRD Reason Given Def of ⊥ lines Right Angle congruent th. Given Reflexive Prop. SAS congruent Pos.

30. Prove ΔARD ≅ ΔGRD Statement DR ⊥ AG <DRA=90°&<DRG =90° <DRA ≅ <DRG AR ≅ RG DR ≅ DR ΔARD ≅ ΔGRD Reason Given Def of ⊥ lines Right Angle congruent th. Given Reflexive Prop. SAS congruent Pos.

31. More examples Decide whether the triangles are congruent and state the theorem or postulate.

32. SAS

34. SSS