Warm Up 90 + 30 + m<L = 180 120 + m<L = 180 m<L = 60 1. 2. 3. 4. 5. 6. 7z + 6 = 90 7z= 84 z = 12 5y = 90 y = 18 60o 12 18 24 60o 24 AC = 12 + 12 AC = 24 (also, AC = LN) LN = 2(18) – 12 LN = 24 m<C = m<L m<C = 60

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 ______________ side of one triangle are _____________ to two angles and the ____________ side of a second triangle, then the two triangles are ________________. included congruent included congruent

Side-Angle-Side (SAS) If two sides and the _____________ angle of one triangle are __________ to two sides and the included angle of a second triangle, then the two triangles are ____________ included congruent congruent

Side-Side-Side (SSS) If 3 sides of one triangle are _____________ to three sides of a second triangle, then the two triangles are ________________. congruent congruent

Angle-Angle-Side (AAS) F A B C D nonincluded If two angles and a _____________________ side of one triangle are _______________ to two angles and the corresponding ____________________ side of a second triangle, then the two triangles are ________________. congruent nonincluded congruent

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!

Other that the “given” information, you can only mark three things. Very Important Other that the “given” information, you can only mark three things. Shared Side (Overlapping Side) or a Shared Angle 2. Vertical Angles 3. Alternate Interior Angles (only if lines parallel).

Shared Side statement reason

Vertical Angles statement reason

Alternate Interior Angles (only if lines parallel) statement 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: A  D, ____________ Use the AAS Congruence Theorem.