Question

Emily says she can prove the Pythagorean Theorem using the following diagram. She explains that she can divide the squares on the two shorter sides into grids with equal-sized grid squares. She says she can then rearrange the grid squares to cover the area of the square on the hypotenuse, which proves that the sum of the squares on the two shorter sides equals the square on the hypotenuse.
A 3 by 3 square, a 4 by 4 square, and a 5 by 5 square, put together to form a right triangle with legs 3 and 4 and hypotenuse 5.

Is this a valid geometrical proof that a2 + b2 = c2 for all right triangles

Answer 1

Answer:

Step-by-step explanation:

This is correct for all right angle because Pythagoras theorem has proved that for a right-angle triangle, the square of the hypotenuse length is equal to the sum of the square of the opposite side and square of the adjacent sides

c² = a² + b²

This is true because the squares formed a right angle triangle from their arrangements.

So, let proved with the formula

Let assume one square = 1 unit

A 3 by 3 Square

Length = 3

A 4 by 4 Square

L = 4

A 5 by 5 Square. Hypotenuse

L = 5

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

Proved, so for all right angle triangles, it is valid