Warm Up on Desk Do Daily Quiz

1. Warm Up on DeskDo Daily Quiz

2. 5.5 ESSENTIAL QUESTION • How do you show and use corresponding parts of congruent triangles are congruent (CPCTC) to prove triangles congruent?

3. Ways to Prove Triangles Congruent • SSS • SAS • ASA • AAS & if Right Triangles, then • HL

4. Ways to Prove Triangles Congruent • SSS • SAS • ASA • AAS & if Right Triangles, then • HL How many Parts do we NEED????

5. Ways to Prove Triangles Congruent • SSS • SAS • ASA • AAS & if Right Triangles, then • HL How many Parts do we NEED???? 3 2

6. Example 1 In the diagram, AB and CD bisect each other at M. Prove that A B. Use Corresponding Parts

7. Example 1 Statements Reasons 1. AB and CD bisect each other at M. 2. MA  MB 2. Definition of segment bisector 3. AMD BMC 3. Vertical Angles Theorem 4. MD  MC 4. Definition of segment bisector 5. ∆ADM ∆BCM 5. SAS Congruence Postulate 6. A B 6. Corresponding parts of congruent triangles are congruent. Use Corresponding Parts 1. Given

8. Example 2 PRACTICE: I do…. Tell what theorem or postulate you can use to show∆JGH  ∆KHG. SOLUTION 1. Visualize Overlapping Triangles MarkGJH HKG andJHG KGH. Sketch the overlapping triangles separately.

9. Example 2 Add congruence marks to GHin each triangle. 3. You can use the AAS Congruence Theorem to show that∆JGH ∆KHG. Visualize Overlapping Triangles 2. Mark all congruent parts!

10. Example 3 Write a proof that shows ABDE. ABC DEC CB CE AB DE 1. Sketch the triangles separately. Use Overlapping Triangles We Do…. SOLUTION Mark all congruent parts!

11. Example 3 1. Given Statements Reasons 1. ABCDEC 2. CB  CE 2. Given 3. C C 3. Reflexive Prop. of Congruence 4. ∆ABC∆DEC 4. ASA Congruence Postulate 5. AB DE 5. Corresponding parts of congruent triangles are congruent. Use Overlapping Triangles Show∆ABC∆DEC to prove thatABDE.

12. Checkpoint 1. Tell which triangle congruence theorem or postulate you would use to show that ABCD. SAS. ANSWER Use Overlapping Triangles More Practice: You do….

13. Checkpoint 2. Prove and show that the triangles or corresponding parts are congruent. GivenKJ KLandJ L, showNJML. Use Overlapping Triangles

14. Checkpoint 1. Given ANSWER 2. Given Statements Reasons 1. KJKL 2. J L 3. K K 3. Reflexive Prop. of Congruence 4. ∆KJN∆KLM 4. ASA Congruence Postulate 5. NJ ML 5. Corresponding parts of triangles are . Use Overlapping Triangles

15. Checkpoint 3. Given SPR QRPand Q S, Prove & show: ∆PQR ∆RSP. Use Overlapping Triangles

16. Checkpoint 1. Given 2. Given ANSWER Statements Reasons 1. SPRQRP 2. Q S 3. PR  RP 3. Reflexive Prop. of Congruence 4. ∆PQR∆RSP 4. AAS Congruence Theorem Use Overlapping Triangles

17. Hw 5.5A

18. Review

19. Determine whether you can use the HL Congruence Theorem to show that the triangles are congruent. Explain your reasoning. 1. 2. ANSWER ANSWER Yes; HL Congruence Theorem can be used. No; there is no information

20. 3. ANSWER Emile could show that the guy wires have equal length Emile and his team have erected this cellphone tower and supporting guy wires. Explain how he could use the HL Congruence Theorem to show that the guy wires are attached to the ground at equal distances from the base of the tower.