Unit 5 · Triangle Congruence and ProofProof-based

5.5HL Congruence

Quick Answer

HL (Hypotenuse-Leg): applies only to right triangles. If the hypotenuse and one leg of one right triangle are congruent to those of another, the triangles are congruent.

Essential Question

Why does HL work as a congruence shortcut for right triangles when SSA does not work in general?

Learning Goals

  • 1State the HL Congruence Theorem and its conditions.
  • 2Identify the hypotenuse and legs of a right triangle.
  • 3Apply HL in proofs involving right triangles.
  • 4Explain why HL is a special case that works only for right triangles.

Key Vocabulary

HL Congruence Theorem

If the hypotenuse and one leg of a right triangle are congruent to those of another right triangle, the triangles are congruent.

Hypotenuse

The side opposite the right angle in a right triangle; the longest side.

Leg (right triangle)

Either of the two sides that form the right angle.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.