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

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

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.

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.” CCCCan also be stated as HL (*corresponding steps*) in proofs.

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

Sample Problem AB C D Problem 1 Given: { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/12/3543703/slides/slide_5.jpg", "name": "Sample Problem AB C D Problem 1 Given:

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. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/12/3543703/slides/slide_6.jpg", "name": "Sample Problem 2 Problem 2 Given: AH HT AH HM H is the midpoint of MT.", "description": "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.

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

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

Video Tutorial

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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