Concept
(1)
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. Applying the Pythagorean Theorem shows that only one value is possible for the other leg. Therefore, the two triangles are also congruent by the SAS or SSS congruence shortcut.
Sample Problems
(3)
Need help with "HL" problems? Watch expert teachers solve similar problems to develop your skills.
Problem 1
How to use the hypotenuse-leg (HL) shortcut to determine the congruence of vertical triangles and how to correctly denote the congruence.
Problem 2
How to use HL to determine the congruence of adjacent right triangles and how to correctly denote the congruence.
Problem 3
How to solve for a variable to make two right triangles congruent using the HL shortcut.
