In a right triangle, the length of two right angles is a, B, the length of the hypotenuse is C, and the height of the hypotenuse is h. It is proved that 1 / a Λ 2 + 1 / b Λ 2 = 1 / h Λ 2 It is suggested that h = AB / C

In a right triangle, the length of two right angles is a, B, the length of the hypotenuse is C, and the height of the hypotenuse is h. It is proved that 1 / a Λ 2 + 1 / b Λ 2 = 1 / h Λ 2 It is suggested that h = AB / C

The Pythagorean theorem has a ^ 2 + B ^ 2 = C ^ 2, so 1 / A ^ 2 + 1 / b ^ 2 = (a ^ 2 + B ^ 2) / (AB) ^ 2 = (C / AB) ^ 2 = 1 / h ^ 2

Cut the square into three pieces and put them together: 1: isosceles right triangle 2: isosceles triangle without right angle 3: isosceles triangle without right angle
Every painting method

1
Square ABCD, connect BD, make AE, vertical BD to e, cut into three pieces and form isosceles right triangle
two
Square ABCD, take AE = DF = ad / 4 on ad, connect be and CF, and cut them into three non right angle isosceles triangles
three
Square ABCD, take a point E on ad, e can't be the midpoint of AD,
Then take the midpoint g of AE and the midpoint h of ED, connect BG and CH, and cut them into three pieces to form a non right angle non isosceles triangle

The area of an isosceles right triangle is 20 cm2. Make the largest square and find the area of the square

20 △ 2 = 10 (cm2)
An isosceles right triangle makes the largest square in it
A vertex of a square is the midpoint of the hypotenuse of a right triangle