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**Ways to Prove Triangles Congruent**

HL Method

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**4 Known Methods Side – Angle – Side (included Angle)**

Angle – Side – Angle (included Side) Angle – Angle – Side Side – Side – Side PLUS ONE MORE!!!

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**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)

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**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)

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

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

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**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.

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

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**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.

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**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!

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