Chapter 8.2, Problem 1CE

To determine

To Define: Draw a diagram for Pythagoras theorem related to area of a square on the legs and the hypotenuse.

Answer to Problem 1CE

The required diagram is,

  

Explanation of Solution

Given information: According to the Pythagoras theorem, the area of the square on the hypotenuse of a right triangle equals to the sum of the areas of the squares on the legs.

According to the Pythagoras theorem,

  $A{B}^2=B{C}^2+A{C}^2$ .

Represent AB, BC, and AC in above equation by lengths c, a, and b respectively, we can write −

  $c^2=a^2+b^2$ ,

where $a^2$ and $b^2$ denotes the areas of squares on the legs of the above right angled triangle, and $c^2$ denotes the area of the square on the hypotenuse of the same triangle.

Therefore, in any right angled triangle, areas of the square drawn from the hypotenuse is equal to the sum of the areas of the squares that are drawn from the two legs, which is shown in the following diagram: