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HL - Problem 1
The hypotenuse-leg (HL) shortcut to determine if two triangles are congruent can be used when both triangles have right angles. The hypotenuse of a right triangle is the side of the triangle opposite the right angle. If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the two triangles are congruent. Remember to name the triangles with the letters in the corresponding positions.
When you are trying to determine if two triangles are congruent and you see a 90 degree angle, you should instantly be thinking hypotenuse-leg short-cut. Can we use it for these two triangles? Well we have vertical angles here which means that this angle must be 90 degrees as well.
So I have in a 90 degree angle triangle, we have a hypotenuse that are congruent in both of these triangles and we have two legs that are congruent. So now we have to determine what is going to be our corresponding vertices.
Well A corresponds to either D or E. But how do I know which it corresponds to? Well AC that line segment has one congruence mark. CD does not have a congruence mark. CE does, which means angle A must correspond to angle E. So I’m going to write angle E first.
Angle B has to correspond angle D then, how do I know that? Because angle C is going to correspond to angle C, so I’m going to write that B corresponds with D. And last our missing angle is C.
So we’ve said that these two triangles are congruent. That’s probably only good enough for half credit. You have to say your congruence short-cut. And we said that we have a right triangle and the hypotenuse and leg were both corresponding and congruent, so we are going to say by HL.