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Hypotenuse Leg Theorem

Proving Congruent Right Triangles

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.

Hypotenuse Leg Worksheet
Theorems and Postulates for proving triangles congruent
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Worksheets & Activities on Triangle Proofs

Example 1
Given AB = XZ, AC = ZY,

ACB =

ZYX = 90°
Prove

ABC

XYZ

ABC and XZY are right triangles since they both have a right angle
AB = XZ (hypotenuse) reason: given
AC = ZY (leg) reason: given
ABC XYZ by the hypotenuse leg theorem which states that two right triangles are congruent if their hypotenuses are congruent and a corresponding leg is congruent.

Hypotenuse Leg Theorem

The following proof simply shows that it does not matter which of the two (corresponding) legs in the two right triangles are congruent.

Example 2
Given AB = XZ, CB = XY,

ACB =

ZYX = 90°
Prove

ABC

XYZ

ABC and XZY are right triangles since they both have a right angle
AB = XZ (hypotenuse) reason: given
CB = XY (leg) reason: given
ABC XYZ by the hypotenuse leg theorem which states that two right triangles are congruent if their hypotenuses are congruent and a corresponding leg is congruent.

Hypotenuse Leg Theorem Example

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