Supplies Needed Giant Whiteboard Marker Eraser WarmUp Which

Supplies Needed: Giant Whiteboard, Marker, Eraser Warm-Up Which congruence shortcut, if any, can be used to prove the triangles congruent? 2. 1. None 3. SSS 4. HL none

E B C A D Which one do you want to see first? • Paragraph proof • Two-column proof • Flow-chart proof

Check Homework

Paragraph Proof Just write, using complete sentences, a logical argument that proves what you want to prove. For everything you state, you must say how you know it.

Paragraph Proof E B C A D

Two-Column Proof Organizes your proof into columns. One column is for your statements, and the other one is for your reasons. The last statement will always be the one you are trying to prove.

Two-Column Proof B Statement A 1) ______ Reason A Given 1) ______ A 2) ______ Vertical Angles Thm. 2) ______ S 3) ______ Given 3) ______ 4) ______ AAS 4) ______ C D

Flow Chart Proof A visual depiction of your proof. Each “bubble” will have a statement and a reason in it. You draw arrows to show which statements lead to which other statements.

Flow-Chart Proof E B C A D

M J K L

M Two-Column Proof J Statement Reason 1) ______ Reflexive Property 1) ______ 2) ______ Given 2) ______ 3) ______ Given 3) ______ 4) ______ Definition of midpoint 4) ______ 5) ______ SAS 5) ______ K L

Flow-Chart Proof M J K L

P Q R S

W Z X Y

B E C A D

Write a flowchart proof! Given: JL bisects KLM Prove: JKL JML

Write a Two-Column Proof Given: C is the midpoint of BD and AE. Prove: ∆ABC ∆EDC

Statements Reasons 1. C is mdpt. of BD and AE 1. Given 2. AC EC; BC DC 2. Def. of mdpt. 3. ACB ECD 3. Vert. s Thm. 4. ABC EDC 4. SAS

CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent. ” It can be used as a justification in a proof after you have proven two triangles congruent.

Remember! SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent.

Write a Flowchart Proof! Given: YW bisects XZ, XY ZY. Prove: XYW ZYW Z

ZW WY Z

Write a Two Column Proof! Given: NO || MP, N P Prove: NMO POM

Statements Reasons 1. N P 1. Given 2. NO || MP 2. Given 3. NOM PMO 3. Alt. Int. s Thm. 4. MO 4. Reflex. Prop. of 5. ∆MNO ∆OPM 5. AAS 6. NMO POM 6. CPCTC

Proofs Worksheet

Write a Two-Column Proof! Given: BC || AD, BC AD Prove: ∆ABD ∆CDB Statements Reasons 1. BC AD 1. Given 2. BC || AD 2. Given 3. CBD ADB 3. Alt. Int. s Thm. 4. BD 4. Reflex. Prop. of 5. ∆ABD ∆ CDB 5. SAS

Write a Two-Column Proof Given: QP bisects RQS. QR QS Prove: ∆RQP ∆SQP Statements Reasons 1. QR QS 1. Given 2. QP bisects RQS 2. Given 3. RQP SQP 3. Def. of angle bisector 4. QP 4. Reflex. Prop. of 5. ∆RQP ∆SQP 5. SAS

Write a Two Column Proof! Given: J is the midpoint of KM and NL. Prove: LKJ NMJ

Statements 1. J is the midpoint of KM and NL. Reasons 1. Given 2. KJ MJ, NJ LJ 2. Def. of mdpt. 3. KJL MJN 3. Vert. s Thm. 4. ∆KJL ∆MJN 4. SAS 5. LKJ NMJ 5. CPCTC