Which two triangles are congruent by the HL theorem? The diagrams are not to scale.

Accepted Solution

Answer: Triangle (a) and Triangle (b) are congruent by the HL Theorem

Rephrased another way: Triangle ABC is congruent to triangle FED by the HL Theorem.



The segment AC is the same length as segment FD. Notice how these two segments have the same number of tickmarks (three tickmarks) to indicate they are congruent segments.

Similarly, BC = ED because of the double-tickmarks shown on those segments.


The fact that BC = ED means we have a pair of corresponding hypotenuses that are congruent (hence the H in HL)

The pairing AC = FD are the two pairs of corresponing legs (the L in HL)

So we have enough to use the HL (hypotenuse leg) theorem. This theorem only works for right triangles. 

1) A right angle is 90 degrees as shown by the square markers for angles A, F, and H
2) The hypotenuse is always opposite the right angle; as the hypotenuse is always the longest side of the right triangle. The largest side is opposite the largest angle.