Why HL Works
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 29 of 63.
HL is SSS in disguise. In a right triangle the Pythagorean theorem ties the three sides together: leg² + leg² = hypotenuse². So once the hypotenuse and one leg are known, the other leg is fixed.
Here 5^2 + b^2 = 13^2, so b^2 = 169 - 25 = 144. Every right triangle with hypotenuse 13 and a leg of 5 has its other leg equal to 12. Two such triangles have three equal pairs of sides, and SSS makes them congruent. That is why HL can skip the third side.
Challenge
Right triangle LMN has hypotenuse MN of 17 and leg LM of 8. Find the other leg LN, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Congruence & Proof
1What a Proof Is
Given and ProveStatements and ReasonsChaining Equal PartsYour First Full ProofRecap: A Chain of Reasons2Congruent Triangles
Same Size, Same ShapeMatching SidesMatching AnglesWhat Congruence GivesRecap: Matching Parts8Proofs with Vertical Angles
Vertical Angles in ProofsThe BowtieBowtie with ASALinear Pairs in ProofsRecap: Vertical Angles