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

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

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

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

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

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

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

13. Checkpoint
Use Overlapping Triangles 2.
Given KJ  KL and J  L,
show NJ  ML.
Prove and show that the triangles or corresponding parts are congruent.

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

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

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

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
No; there is no information
ANSWER
Yes; HL Congruence Theorem can be used.

20. 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. 3.
ANSWER
Emile could show that the guy wires have equal
length