Ways to Prove Triangles Congruent HL Method

4 Known Methods Side – Angle – Side (included Angle) Angle – Side – Angle (included Side) Angle – Angle – Side Side – Side – Side PLUS ONE MORE!!!

Hypotenuse-Leg (HL Method) Only works with a right triangle Must have a right angle Hypotenuses must be congruent Must also have one additional side (leg)

The 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)

Must both have right angles, congruent legs and congruent hypotenuses.

Example of HL Method * Would otherwise have been SSA except for the right angle.

Corresponding 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.

  Hint! List the first three for congruence, then list the second three.

We 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 = XZ AC = YZ and <B = <X Hint! List the first three for congruence, then list the second three.

CPCTC often used in proofs Given: BO=MA OW=AN BW=MN Prove: ∠O=∠A Statements Reasons BO=MA Given OW=AN BW=MN ∆BOW=∆MAN SSS Method of Congruence ∠O=∠A CPCTC * CPCTC always comes AFTER the congruence statement!