Welcome Proof Experts!

1. Welcome Proof Experts! • Pick up notes and take out your homework • Take out your Transformation Test Corrections ( if you didn’t turn it in last week) Tonight’s HW: • P 262 #1-4, 7-11 • Study guide # 1-8 ( skip 6, 7) • Make notecards from U2L10 and U2L11 (definition one side and vocab. word on the other side UPDATES: • Unit 2 Test is on Thursday/Friday

2. Agenda • Review HW • 4.6: CPCTC • Notecard Practice! • Begin 4.8: Isosceles and Equilateral Triangles

3. Review HW On document camera

4. 4-6 Triangle Congruence: CPCTC Learning Objective: • Use CPCTC to prove parts of triangles are congruent.

5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) • It is used to prove the remaining pieces of a triangle are congruent after you have proved that two triangles are congruent. • Similar to when we used ______________ to prove that two lines are ________________.

6. Example 1 Some hikers come to a river in the woods. They want to cross the river but decide to find out how wide it is first. So they set up congruent right triangles. The figure shows the river and the triangles. Find the width of the river, GH. ( write small!) Lets first prove that the two triangles are congruent. Use a 2- column proof.

7. Whiteboards A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK? First prove that the two triangles are congruent. The two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so JK = 41 ft.

8. Whiteboards Fill in the blanks

9. Given:PR bisects QPS and QRS. Prove:PQ  PS Example 2 Write this proof in two different ways.

10. QRP SRP QPR  SPR PR bisects QPS and QRS RP PR Reflex. Prop. of  Def. of  bisector Given ∆PQR  ∆PSR ASA PQPS CPCTC Example 2Continued

11. Given:J is the midpoint of KM and NL. Prove:KL || MN Example 3

12. 1.J is the midpoint of KM and NL. 2.KJ  MJ, NJ  LJ 6.KL || MN Example 3 Continued Statements Reasons 1. Given 2. Def. of mdpt. 3. KJL  MJN 3. Vert. s Thm. 4. ∆KJL  ∆MJN 4. SAS Steps 2, 3 5. LKJ  NMJ 5. CPCTC 6. Conv. Of Alt. Int. s Thm.

13. Whiteboards

14. Math Joke of the Day What do you write as the reason when using corresponding parts of congruent triangles in a proof? • See Peas Eat Easy! ( CPCTC)

15. King/Queens’ Court • I don’t want to stand up here all period and do proofs so we are going to play a game! • You are competing against everyone in the classroom to be the first to finish. • If you finish you will come to the front board and compete against all of the students in the class.

16. King/Queens’ Court • I am going to post a question on the board. • When you finish, raise your board. • If you are right, you become the king/queen. • If you are wrong you must wait for two other students to raise their board before you can raise yours again.

17. King/Queens’ Court • QUESTIONS?!?

18. ROUND 1

19. ROUND 2 Find the measure of the question mark.

20. ROUND 3

21. ROUND 4 Find the measure of the question mark.

22. ROUND 5

23. Notecard Practice Practice with your partner. You need to be on task. During this time, I will walk around to make sure you are • On task • Made notecards