In these lessons, we will learn
- the Hypotenuse-Leg Theorem
- why the Hypotenuse-Leg Theorem is enough to prove triangles congruent
- the proof of the Hypotenuse-Leg Theorem using a two-column proof
- how to prove triangle congruence using the Hypotenuse-Leg Theorem
Related Topics: More Geometry Lessons
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
- ΔABC and ΔPQR are right triangles
- AC = PQ (hypotenuse)
- AB = PR (leg)
So, triangle ABC
and triangle PQR
are congruent by the Hypotenuse Leg Theorem.
Hypotenuse - Leg Congruence Theorem
Explains why HL is enough to prove two right triangles are congruent using the Pythagorean Theorem
The following video shows more examples of the Hypotenuse Leg (HL) Theorem and the Angle-Angle-Side (AAS) Theorem
Prove Triangle Congruence with HL Postulate
HL Postulate (Lesson)
A lesson and proof of the HL (Hypotenuse-Leg) postulate using a two-column proof
HL Postulate (Practice)
Practice problems and proofs using the HL (Hypotenuse-Leg) Postulate
You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.
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