Question

Why does the LL theorem hold for proving right triangles congruent?

Answer 1

The correct answer is:

The LL theorem states that if the two legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent.

The third side of a right triangle is the hypotenuse. Using the Pythagorean theorem, we know that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. Based on the LL theorem, we know that the legs are congruent; this means the sum of the squares of these legs would be the same in both triangles, which would give us the same hypotenuse.

Now we have all 3 sides congruent, so we can use the SSS, or side-side-side, theorem to prove congruence.

Answer 2

Triangles, considering congruent triangles, are generally composed of 2 sides and a hypotenuse. The hypotenuse is usually between these 2 sides. The best possible explanation is that the right angle is included between the legs. Using the "L" shape in the "LL" theorem, it is side then right angle then side to prove congruence between triangles.