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HL - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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.

A lesser used congruent shortcut for determining if two triangles are congruent is what's known as hypotenuse leg, or abbreviated hl. This only applies to right triangles so let's say I had these two triangles and I'm trying to determine if they're congruent. Well some new words that you might not have heard are leg and hypotenuse. Notice the legs are the two sides that are adjacent to your 90 degree angle. The hypotenuse is the side that is opposite the 90 degree angle so that's going to be your longest side in your triangle. If you have enough information then you can say that these two triangles are congruent. But I said hypotenuse leg so that means if I tell you that these two hypotenuse I is I guess how you might say it if those two are congruent and if one of these legs are congruent then yes you can say that these two triangles must be congruent. You can also look for the other set of legs so let's say I didn't know anything about these two sides and I told you that these two legs were congruent you could still say because of hypotenuse leg in a right triangle these two must be congruent.

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