# Aim: How do we review congruent triangle proofs? DO NOW: List as many ‘reasons’ as you can for congruent triangles.

Triangle Congruence Proofs Practice with CPCTC!
Triangle Congruence Proofs Practice with CPCTC!

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Aim: How do we review congruent triangle proofs? DO NOW: List as many ‘reasons’ as you can for congruent triangles

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LIST OF REASONS 1.Perpendicular lines form right angles 2.All right angles are congruent 3.If 2 angles are congruent their supplements are congruent 4.Reflexive Property 5.Addition Property 6.Subtraction Property 7.If 2 angles are congruent their complements are congruent 8.A midpoint divides a line segment into 2 congruent parts 9.If 2 sides in a triangle are congruent, then opposite angles are congruent 10.A tri-sector divides a line segment into 3 congruent parts 11.Corresponding parts in congruent triangles are congruent (CPCTC) 12.Halves of congruent angles are congruent 13.Halves of congruent line segments are congruent 14.If 2 angles in a triangle are congruent, then opposite sides are congruent 15.If at last two sides of a triangle are congruent, then the triangle is isosceles 16.If a triangle contains a right angle, it is a right triangle

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Practice Proof 1 StatementReason 1. BA=DC 2. BD bisects AC 3. AC Bisects BD 4. BE=ED 5. AE=EC 1. Given 2. Given 3. Given 4. A bisector divides a line segment into 2 equal parts 5. ” 6. ABE=CDE6. SSS=SSS

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Ways to prove triangles SAS Side-Angle-Side AAS Angle-Angle-Side ASA Angle-Side-Angle SSS Side-Side-Side

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REMEMBER! The Donkey Theorem ASS (SSA) DOES NOT PROVE TRIANGLES CONGRUENT! Also: AAA only proves triangles similar, and not congruent! HY-LEG (Which is the hypotenuse and a leg) can only be used in RIGHT TRIANGLES!

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Proof #2 StatementReason 1. <D=<A 2. <BCD=<BCA 3. BC=BC 4. ABC=DBC 1. Given 2. Given 3. Reflexive 4. AAS=AAS

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Pair Share! Yay 🙂 Given: Line RP Bisects angle QRS and QPS Prove: Triangle PRS =Triangle PQR StatementReason 1. RP Bisects QRS and QPS 2. QPR=SPR 3. PRQ=PRS 1. Given 2. Bisector divides an angle into two = parts 3. “ 4. PR=PR 5. Triangle PRS=Triangle PQR 4. Reflexive 5. ASA=ASA

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Another Pair Share? StatementReason 1. SU=VW 2. SW Bisects UV 3. UV Bisects SW 4. Triangle SUT=VTW 5. OR 6. <STU=<VT W 1. Given 2. Given 3. Given 4. SSS=SSS 5. Vertical Angles are congruent ^ That’s supposed to be Triangle SUT=VTW Sorry! 🙂

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Homework :’( The homework can be found on the other side of your Reasons handout! Have fun? Good luck on the Regents!~

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