1. 3.8 - The HL Postulate By: David Galaydick Mike Pettinato Matt Pettinato

2. 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.

3. 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.

4. 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

5. Sample Problem AB C D Problem 1 Given: <ABC and <BCD are right angles. AC BD Prove: ABC DCB Statements Reasons 1.<ABC and <BCD are right angles 2.AC BD 3.BC BC 4. ABC and DCB are right s 5. 1.Given 2.Given 3.Reflexive 4. If a triangle contains a rt<, then it is a rt. ABC DCB5. HL ( 2,3,4)

6. 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.<AHM and <AHT are rt <s 5.MH MT 6.AM AT 7. AHM and AHT are rt s 8. AHM AHT 1.Given 2.Given 3.Given 4. lines form rt <s 5.Mdpts. divide segs. into 2 segs. 6.All radii of a circle are 7. If a contains a rt < then it’s a rt 8. HL (5,6,7)

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

8. 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

9. Video Tutorial

10. 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