The HL Rule
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 28 of 63.
SSA does not prove congruence in general, but one case is special: when the angle is a right angle. Two right triangles with equal hypotenuses and one pair of equal legs are congruent. The rule is HL, hypotenuse leg.
| Statement | Reason |
|---|---|
| 1. ∠QPR is a right angle | Given (the square) |
| 2. ∠YXZ is a right angle | Given (the square) |
| 3. QR = YZ | Given |
| 4. RP = ZX | Given |
| 5. △PQR ≅ △XYZ | HL, using lines 1 to 4 |
Both right angles must be known: HL is a rule about right triangles. The squares on the figure count, and writing them as lines makes the proof easy to read.
Challenge
△ABC and △DEF have right angles at A and D. The ticks show BC = EF and AB = DE. Prove that △ABC ≅ △DEF, then press Check.
Try it yourself
Write the proof
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