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3.8 - The HL Postulate By: David Galaydick Mike Pettinato Matt Pettinato

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What is it? HL stands for hypotenuse leg. It is used for proving right triangles congruent. It can be used to prove something congruent, but it is only treated as a postulate. Only applies to right triangles. No other types.

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The Postulate T T T The postulate states: “If there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent.” CCCCan also be stated as HL (*corresponding steps*) in proofs.

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Using the HL Postulate The desired triangles must first be proven as right triangles. (If a triangle contains a right angle, then it is a right triangle.) Hypotenuse – The longest side of a triangle opposite of a right angle. Hypotenuses of each triangle must be proven congruent. Any leg of the two triangles must be proven congruent. Can also be the leg

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Sample Problem AB C D Problem 1 Given:

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Sample Problem 2 Problem 2 Given: AH HT AH HM H is the midpoint of MT. A Prove: AHM AHT A M T H Statements Reasons 1.AH HT, AH HM 2. H is the midpoint of MT 3. A 4.

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Practice Problem 1 G N A R Y L Given: GR AL NA GL RY GL Prove: GNA LYR Statements Reasons

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Practice Problem 2 P L U G E R S Given: PUG is isosceles w/ base PG UN UL PR EG EL PU RN UG Prove: LE RN N Statements Reasons

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Video Tutorial

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Works Cited Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston: McDougal Little & Company, 1991. Print. Image from Microsoft clip art

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