1. Do Now: Signed progress Reports put in the basket
Pick up the guided notes and take out your HW for Ms. Taylor to stamp
The other worksheet you picked up, read the problem, on the back are “coaching questions.” Answer each Coaching questions and hand it into the basket
Then solve this:

2. Proofs for Triangles

3. Proofs
Follow a problem step-by-step with justification or reasoning for each step.
2-Column Proofs
Flow Chart Proofs

4. General Format
For proofs, we will be given 2 statements; the GIVEN and PROVE
Always start with the Given information
We end the proof with the Prove statement
The reason for each step is an explanation as to HOW you got the information from previous steps

5. 2-Column Proofs
One Column is titled “Statements” and the other “Reasons”
Any statement must come from the given information, the picture, or come from previous steps
Statement
Reason
1. YA≌AB
1. Given
2. <Y≌<B
2. Given
3. <YAZ≌<CAB
3. Vert. < Thm.
4. ∆ZAY≅ ∆CAB
4. ASA Postulate
5. ZA≅AC
5. CPCTC
Just An
example

6. Write a 2-Column Proof 1. 2. 3. 4. 5. 6. Statements Reasons
Given: 5 + 2(y + 4) = 5(y - 3) + 10
Prove: y = 6
Statements
Reasons 1. 2. 3. 4. 5. 6.

7. Flow Chart Proofs
You can start a column with any of the following information
Given
Reflexive Statements
Information from the picture
Flow Chart proofs have lines connecting related information
The statements are in the bubbles, and the reasons are written below.

8. Given: KJ ≅ MN, <J ≅ <N Prove: ∆KJL ≅ ∆MNL

9. SSS (2-Column) 1. MO≌LK and KM≌OL Given 2. KO≌KO Reflexive
Given: MO≌LK and KM≌OL
Prove: ∆KOM ≌ ∆OKL
Statements Reasons
1. MO≌LK and KM≌OL Given
2. KO≌KO Reflexive
3. ∆KOM ≌ ∆OKL SSS Postulate

10. SSS Flowchart Proof
Given: MO≌LK and KM≌OL
Prove: ∆KOM ≌ ∆OKL

11. ASA (2-Column) Given: <Y≅<B and YA≅BA Prove: ∆ZAY≅ ∆CAB
Statements Reasons
1. <Y≅<B and YA≅BA Given
2. <ZAY≅<CAB Vertical < Thm
3. ∆ZAY≅ ∆CAB ASA Postulate

12. ASA Flowchart
Given: <Y≅<B and YA≅BA
Prove: ∆ZAY≅ ∆CAB

13. Fill in the Missing Info!
Given: DA≅MA, AJ≅AZ
Prove:∆ JDA  ∆ ZMA

14. CPCTC: Corresponding Parts of Congruent Triangles are Congruent CPCTC

15. Definition of Congruent Triangles
If two triangles corresponding parts are congruent, then the triangles are congruent.
This allows us to use the congruent triangle methods (SSS, ASA, SAS, AAS, HL)
If two triangles are congruent, then their corresponding parts are congruent.
This is where we use CPCTC. Use after we have found SSS, ASA, SAS, AAS, HL

16. In a proof…
Use congruent parts to determine SSS, ASA, SAS, AAS, HL to show two triangles are congruent.
Then use CPCTC to show corresponding parts of the same triangles are congruent.

17. When do we use CPCTC? Given: YA≌AB, <Y≌<B Prove: ZA≌AC Statement
Reason
1. YA≌AB
1. Given
2. <Y≌<B
2. Given
3. <YAZ≌<CAB
3. Vert. < Thm.
4. ∆ZAY≅ ∆CAB
4. ASA Postulate
5. ZA≅AC
5. CPCTC

18. Classwork
Complete the proofs on the back of the last page of notes!

23. Homework
Quiz Review Sheet (front only)
Finish proofs on notes