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Ways to Prove Ways to Prove Triangles CongruentTriangles Congruent
HL Method
4 Known Methods4 Known Methods
Side – Angle – Side (included Angle)Angle – Side – Angle (included Side)Angle – Angle – SideSide – Side – Side
PLUS ONE MORE!!!
Hypotenuse-Leg Hypotenuse-Leg (HL Method)(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 Corresponding Parts of Congruent Triangles are Congruent Triangles are
CongruentCongruent(CPCTC)(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.
Hint! List the first three for congruence, then list the second three.
We know that ∆ABC and ∆XYZ are congruent by the AAS method. What are the other three corresponding parts?
BC = XZAC = YZand <B = <X
CPCTC often used in proofsCPCTC often used in proofs
Statements Reasons
BO=MA Given
OW=AN Given
BW=MN Given
∆BOW=∆MAN SSS Method of Congruence
∠O=∠A CPCTC
Given: BO=MAOW=ANBW=MN
Prove: ∠O=∠A
* CPCTC always comes AFTER the congruence statement!
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