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Warm Up 90 + 30 + m<L = 180 120 + m<L = 180 m<L = 60 7z + 6 = 90 7z= 84 z = 12 1. 4. 12 24 LN = 2(18) – 12 LN = 24 5y = 90 y = 18 2. 5. 18 60o m<C = m<L m<C = 60 3. 60o 6. 24 AC = 12 + 12 AC = 24 (also, AC = LN) Marking Congruent Triangles Thm. Corresponding Parts of Congruent Triangles are Congruent (CPCTC) If two triangles are congruent, then their corresponding parts are congruent. Angle-Side-Angle (ASA) If two angles and the ______________ included side of one congruent triangle are _____________ to two angles and the ____________ side of a second triangle, then the included congruent two triangles are ________________. Side-Angle-Side (SAS) If two sides and the _____________ included angle of one triangle are __________ congruent to two sides and the included angle of a second triangle, then the two triangles are ____________ congruent Side-Side-Side (SSS) congruent to If 3 sides of one triangle are _____________ three sides of a second triangle, then the two congruent triangles are ________________. Angle-Angle-Side (AAS) E A F B C D nonincluded If two angles and a _____________________ side of one congruent to two angles and the triangle are _______________ nonincluded corresponding ____________________ side of a second congruent triangle, then the two triangles are ________________. Hypotenuse-Leg (HL) If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent . Does AAA work? Does AAA work? NO! Does ASS work? No! There is no ASS in geometry! Very Important Other that the “given” information, you can only mark three things. 1.Shared Side (Overlapping Side) or a Shared Angle 2. Vertical Angles 3. Alternate Interior Angles (only if lines parallel). Shared Side D A B statement C reason Vertical Angles statement reason Alternate Interior Angles (only if lines parallel) E statement B C D A reason Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS Decide whether the triangles are congruent. Explain your reasoning. Yes, AAS Decide whether the triangles are congruent. Explain your reasoning. Yes, SAS Decide whether the triangles are congruent. Explain your reasoning. No, SSA doesn’t work! Decide whether the triangles are congruent. Explain your reasoning. Yes, AAS Ex. State the third congruence that must be given to prove ABC DEF. GIVEN: AC DF , A D, ____________ Use the AAS Congruence Theorem.