# PROVING THE PYTHAGOREAN THEOREM WORKSHEET

## About "Proving the pythagorean theorem worksheet"

Proving the pythagorean theorem worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on "Pythagorean theorem".

## The Pythagorean Theorem

In a right triangle, the sum of the squares of the lengths of the  legs is equal to the square of the length of the hypotenuse.

If a and b are legs and c is the hypotenuse, then

a² + b²  =  c²

## Proving the pythagorean theorem worksheet - Problems

1. In the right triangle given below, prove the Pythagorean theorem.

2. In the right triangle given below, prove the Pythagorean theorem.

3. In the right triangle given below, prove the Pythagorean theorem.

4. In the right triangle given below, prove the Pythagorean theorem.

## Using pythagorean theorem worksheet- Solution

Problem 1 :

In the right triangle given below, prove the Pythagorean theorem.

Solution :

Step 1 :

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b²  =  c²

Step 2 :

In the above right triangle,

a  =  7, b  =  24 and c  =  25

Step 3 :

Find the value of a² + b².

a² + b²  =   + 24²

a² + b²  =  49 + 576

a² + b²  =  625 ----- (1)

Step 4 :

Find the value of c².

=  25²

=  625 ----- (2)

Step 5 :

From (1) and (2), we get

a² + b²  =  c²

Problem 2 :

In the right triangle given below, prove the Pythagorean theorem.

Solution :

Step 1 :

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b²  =  c²

Step 2 :

In the above right triangle,

a  =  9, b  =  12 and c  =  15

Step 3 :

Find the value of a² + b².

a² + b²  =  9² + 12²

a² + b²  =  81 + 144

a² + b²  =  225 ----- (1)

Step 4 :

Find the value of c².

=  15²

=  225 ----- (2)

Step 5 :

From (1) and (2), we get

a² + b²  =  c²

Problem 3 :

In the right triangle given below, prove the Pythagorean theorem.

Solution :

Step 1 :

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b²  =  c²

Step 2 :

In the above right triangle,

a  =  40, b  =  30 and c  =  50

Step 3 :

Find the value of a² + b².

a² + b²  =  40² + 30²

a² + b²  =  1600 + 900

a² + b²  =  2500 ----- (1)

Step 4 :

Find the value of c².

=  50²

=  2500 ----- (2)

Step 5 :

From (1) and (2), we get

a² + b²  =  c²

Problem 4 :

In the right triangle given below, prove the Pythagorean theorem.

Solution :

Step 1 :

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b²  =  c²

Step 2 :

In the above right triangle,

a  =  9, b  =  40 and c  =  41

Step 3 :

Find the value of a² + b².

a² + b²  =  9² + 40²

a² + b²  =  81 + 1600

a² + b²  =  1681 ----- (1)

Step 4 :

Find the value of c².

=  41²

=  1681 ----- (2)

Step 5 :

From (1) and (2), we get

a² + b²  =  c²

After having gone through the stuff given above, we hope that the students would have understood "Proving the pythagorean theorem worksheet".

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