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:

Proofs for Triangles

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

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

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

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.

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.

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

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

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

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

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

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

CPCTC: Corresponding Parts of Congruent Triangles are Congruent CPCTC

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

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.

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

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

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