1. Lesson 4-2 Some Ways to Prove Triangles Congruent (page 122) Essential Question Can you construct a proof using congruent triangles?

2. How many triangles do you see? Count the number of triangles that you see. Then ask someone else how many triangles they see and take a second count.

3. # of small ∆’s = 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

4. How many triangles do you see? # of small ∆’s = 16 1 2 3 456 7 # of medium ∆’s = 7

5. How many triangles do you see? # of small ∆’s = 16 1 2 3 # of medium ∆’s = 7 # of large ∆’s = 3

6. How many triangles do you see? # of small ∆’s = 16 1 # of medium ∆’s = 7 # of large ∆’s = 3 # of X-large ∆’s = 1 total ∆’s = 27

7. _______ is opposite ∠ A and … A B C opposite side

8. … ∠ B is opposite _______ A B C

9. ∠ A is the included angle between _____ and _____. A B C included angle

10. is the included side between _____ and _____. A B C ∠A∠A ∠B∠B included side

11. (1) Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆ABC with … AB = 3 cm, BC = 5 cm, and AC = 6 cm. A B C 6 cm 3 cm 5 cm Similar to page 121 #22 (d) SSS

12. (2) Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆DEF with … DE = 3 cm, m ∠ E = 60º, and EF = 4 cm. D F E3 cm 4 cm 60º Similar to page 121 #22 (a) SAS

13. (3) Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆XYZ with … m ∠ X = 30º, XY = 4 cm, and m ∠ Y = 50º. X Z Y 4 cm 30º50º Similar to page 121 #22 (b) ASA

14. OH, just one more: Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆UVW … m ∠ U = 30º, m ∠ V = 50º, and m ∠ W = 100º. U W V 30º50º Similar to page 121 #22 (c) AAA 100º AAA

15. Congruent Triangle Notes 1.If two triangles are congruent, then you know 6 pairs of corresponding parts are also congruent. 2.Based on the prior exercises, 3 pairs of congruent corresponding parts will guarantee that two triangles are congruent.

16. If three sides on one triangle are congruent to three sides of another triangle, then the triangles are congruent. Postulate 12 SSS Postulate

17. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Postulate 13 SAS Postulate

18. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Postulate 14 ASA Postulate

19. Ways to Prove Triangles Congruent 1. SSS Postulate 2. SAS Postulate 3. ASA Postulate Pattern that does NOT Prove △ ’s ≅ 1. AAA Know these patterns! Remember this does NOT work!

20. Ways to Prove Triangles Congruent SSS Postulate SAS Postulate ASA Postulate

21. Know and use the patterns! Classroom Exercises on pages 123 & 124 1 to 11 all numbers

22. Ways to Prove Triangles Congruent 1. SSS Postulate 2. SAS Postulate 3. ASA Postulate Patterns that do NOT Prove △ ’s ≅ 1. AAA 2. SSA Know these patterns! Remember these do NOT work!

23. 4 1 2 H 3 G I StatementsReasons 1.____________________________________ _____________________________________________ 2._________________________________________________________________________________ 3._________________________________________________________________________________ 4._________________________________________________________________________________ Given: Prove: ∆ GHJ  ∆ IJH Proof: Given ∆ GHJ  ∆ IJH ∠ 1  ∠  ∠ 3  ∠  || - lines ⇒ AIA  ASA Postulate Reflexive Property (1) Complete the proof. J

24. Given: Prove: ∆ MOK  ∆ TOK Proof: (2) Complete the proof. K O 1 2 M T

25. Assignment Written Exercises on pages 124 to 127 RECOMMEDED: 19 & 21 REQUIRED: 1 to 17 odd numbers 22, 24, 26 will done in class! Check out my link on Congruent Triangles.Congruent Triangles Prepare for Quiz on Lessons 4-1 and 4-2 Can you construct a proof using congruent triangles?