Presentation on theme: "3.8 - The HL Postulate By: David Galaydick Mike Pettinato Matt Pettinato."— Presentation transcript:
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.” CCCCan 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:
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.
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
Works Cited Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston: McDougal Little & Company, Print. Image from Microsoft clip art