The two right sides of a right triangle are a and B, the length of the hypotenuse is C, and the height of the hypotenuse is h Such as the title

The two right sides of a right triangle are a and B, the length of the hypotenuse is C, and the height of the hypotenuse is h Such as the title

It is known that a * a + b * b = C * C AB = CH (a + b) (a + b) + h * H = a * a + b * B + 2A * B + h * H = C * C + 2CH + h * h, so it is a right triangle

The two right sides of a right triangle 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 C + H, a + B and h as sides

AB = CH (because AB / 2 = ch / 2 = s △ ABC)
A ^ 2 + B ^ 2 = C ^ 2 (because right triangle has Pythagorean theorem)
(c+h)^2=c^2+2ch+h^2
(a+b)^2=a^2+2ab+b^2=c^2+2ch
(c + H) ^ 2 = (a + b) ^ 2 + H ^ 2, so the triangles with their sides are right triangles

Suppose that the lengths of two right angles of a right triangle are a and B, the height of the hypotenuse is h, and the length of the hypotenuse is C, then the shape of the triangle with C + H, a + B and h as sides is ()
A. Right triangle B. acute triangle C. obtuse triangle D. shape cannot be determined by the size of a, B, C

∵ a, B are the two right sides of a right triangle ∵ A2 + B2 = C2 and ∵ h is the height of the hypotenuse, C is the length of the hypotenuse ∵ ch = ab ∵ H2 + (a + b) 2 = H2 + A2 + B2 + 2Ab = H2 + C2 + 2CH, and (c + H) 2 = C2 + 2CH + H2 ∵ H2 + (a + b) 2 = (c + H) 2 ∵ triangle is a right triangle