In these lessons, we will learn
The following diagram shows the Hypotenuse Leg Theorem. Scroll down the page for more examples and solutions of how to use the Hypotenuse Leg Theorem.
Hypotenuse Leg Theorem is used to prove whether a given set of right triangles are congruent.
The Hypotenuse Leg (HL) Theorem states that
If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.
In the following right triangles ΔABC and ΔPQR , if AB = PR, AC = QR then ΔABC ≡ ΔRPQ .
State whether the following pair of triangles are congruent. If so, state the triangle congruence and the postulate that is used.
From the diagram, we can see that
The hypotenuse-leg congruence theorem states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, the two triangles are congruent.
Explains why HL is enough to prove two right triangles are congruent using the Pythagorean Theorem.
Examples of the Hypotenuse Leg (HL) Theorem and the Angle-Angle-Side (AAS) Theorem
State whether or not the following pairs of triangles must be congruent. If so, state the triangle congruence and name the postulate that is used.
HL Postulate (Lesson)
A lesson and proof of the HL (Hypotenuse-Leg) postulate using a two-column proof
Practice problems and proofs using the HL (Hypotenuse-Leg) Postulate
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.