Short answer:
In geometry, “HL” almost always means the Hypotenuse–Leg theorem for right triangles. It says: if two right triangles have the same hypotenuse length and the same leg length, then the triangles are congruent (exactly the same shape and size).

🧠 What is HL in geometry?

When you see “HL” in a geometry problem, it almost always stands for Hypotenuse–Leg :

  • H = Hypotenuse (the longest side of a right triangle, opposite the right angle)
  • L = Leg (either of the two shorter sides that form the right angle)

The HL congruence theorem says:

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

That means the triangles match exactly: all sides and angles line up, even though you only checked one leg + the hypotenuse.

📐 Mini story: How teachers use HL

Imagine your teacher draws two right triangles on the board that don’t look identical at first glance. One is tall and skinny, the other short and wide. But then they say:

  • Triangle 1 and Triangle 2 both have hypotenuse = 10 units.
  • One leg in Triangle 1 is 6 units, and the corresponding leg in Triangle 2 is also 6 units.

Without measuring anything else, you can confidently say:

These two right triangles are congruent by HL.

Even if the drawings look different, the HL theorem guarantees they’re secretly the same triangle in disguise.

🔍 How HL compares to other congruence rules

You might already know other triangle congruence “shortcuts”:

  • SSS – Side–Side–Side
  • SAS – Side–Angle–Side
  • ASA – Angle–Side–Angle
  • AAS – Angle–Angle–Side

HL is special because it only works for right triangles and uses the fact that one angle is already 90°. That’s why it’s sometimes listed separately as a right-triangle rule rather than a general triangle rule.

Some textbooks and sites even call it RHS (Right angle–Hypotenuse–Side) instead of HL, especially outside the U.S.

✅ When can you use HL?

You can use HL when:

  1. You know both triangles are right triangles (each has a 90° angle).
  1. You know the hypotenuse lengths match.
  1. You know one pair of corresponding legs match.

If any of these are missing (for example, you’re not told it’s a right triangle, or the side you know is not the hypotenuse), then HL doesn’t apply , and you should look at SAS, ASA, etc. instead.

🌐 Small note on confusion

You might occasionally see other creative explanations online (like calling HL a “height line”), but in school geometry and most textbooks , HL very clearly refers to the Hypotenuse–Leg theorem for right triangle congruence.

TL;DR

  • HL in geometry = Hypotenuse–Leg theorem.
  • It’s a right triangle congruence rule.
  • If two right triangles have the same hypotenuse and one same leg, the triangles are congruent.

Information gathered from public forums or data available on the internet and portrayed here.