Question

Prove the HL Theorem without angle measures or Pythagorean theorem. cannot include HL theorem in proof

Answer #1

Triangle ABC Triangle DEF

Area of triangle ABC = AB x BC (For right-angle triangle area =
base x height)

Area of triangle DEF = DE x EF

If they are congruent the area is also the same.

AB x BC = DE x EF (One leg of the triangle is the same AB = DE, and
the hypotenuse is also same )

BC = EF

Now, we have all three sides are the same of above two triangles.
Now we can say they are congruent to each other.

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