24 Known Methods Side – Angle – Side (included Angle) Angle – Side – Angle (included Side)Angle – Angle – SideSide – Side – SidePLUS ONE MORE!!!
3Hypotenuse-Leg (HL Method) Only works with a right triangleMust have a right angleHypotenuses must be congruentMust also have one additional side (leg)
4The parts of a Right Triangle * Must have a right angle. * The two acute angles must be complementary.* The two side opposite the acute angles are Legs.* The side opposite the right angle is the Hypotenuse.(the Hypotenuse is always the longest side)
5Must both have right angles, congruent legs and congruent hypotenuses.
6Example of HL Method* Would otherwise have been SSA except for the right angle.
7Corresponding Parts of Congruent Triangles are Congruent (CPCTC) We know that there are six corresponding parts in two congruent triangles.We need THREE to prove that two triangles are congruent.After we prove two triangles congruent, there are 3 additional corresponding parts that are therefore congruent.
8Hint! List the first three for congruence, then list the second three.
9We know that ∆ABC and ∆XYZ are congruent by the AAS method We know that ∆ABC and ∆XYZ are congruent by the AAS method. What are the other three corresponding parts?BC = XZAC = YZand <B = <XHint! List the first three for congruence, then list the second three.
10CPCTC often used in proofs Given: BO=MAOW=ANBW=MNProve: ∠O=∠AStatementsReasonsBO=MAGivenOW=ANBW=MN∆BOW=∆MANSSS Method of Congruence∠O=∠ACPCTC* CPCTC always comes AFTER the congruence statement!