On the Pythagorean theorem in junior high school It is known that the two right angle sides of the RT triangle ABC are a and B, the hypotenuse is C, and the height of the hypotenuse is h. try to judge the shape of the triangle with H, C + H, and a + B as sides Please explain why,

On the Pythagorean theorem in junior high school It is known that the two right angle sides of the RT triangle ABC are a and B, the hypotenuse is C, and the height of the hypotenuse is h. try to judge the shape of the triangle with H, C + H, and a + B as sides Please explain why,

It's a right triangle
A square + b square = C square
(c + H) square = C square + H square + 2CH
(a + b) square = a square + b square + 2Ab = C square + 2Ab
Because in a RT triangle, ab = CH (same area)
Substituting the above formula
We get (a + b) square + H square = (c + H) square
So the new triangle is also a right triangle