Triangle Congruence by HL

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Triangle Congruence by SSS, SAS, ASA and AAS

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Examples, solutions, videos, worksheets, games, and activities to help Geometry students learn triangle congruence by the Hypotenuse Leg (HL) Theorem.

Conditions for the HL Theorem.
To use the HL Theorem, the triangles must meet three conditions.

  1. There are two right triangles.
  2. The triangles have congruent hypotenuses.
  3. There is one pair of congruent legs.

Hypotenuse Leg
In right triangles, if two legs are congruent and if the two hypotenuses are congruent, then the triangles are congruent. This is known as the hypotenuse leg theorem. Note that this is the SSA shortcut which does not apply to non-right triangles.
Hypotenuse - Leg Congruence Theorem

To prove triangles congruent by the hypotenuse leg theorem.

Hypotenuse Leg Triangle Congruence
Proving the Hypotenuse Leg Congruence Theorem using SAS ans AAS.

Write a proof using HL

Congruence in Right Triangles: H-L
Using the H-L theorem to prove two right triangles are congruent

Hypotenuse Leg and Angle Angle Side

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