PROVING THE PYTHAGOREAN THEOREM WORKSHEET

Problem 1 :

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

Problem 2 :

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

Problem 3 :

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

Problem 4 :

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

Answers

1. Answer :

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  =  72 + 242

a2 + b2  =  49 + 576

a2 + b2  =  625 -----(1)

Step 4 :

Find the value of c2. 

c2  =  252

c2  =  625 -----(2)

Step 5 :

From (1) and (2), we get

a2 + b2  =  c2

2. Answer :

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. 

c2  =  152

c2  =  225 -----(2)

Step 5 :

From (1) and (2), we get

a2 + b2  =  c2

3. Answer :

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. 

c2  =  502

c2  =  2500 -----(2)

Step 5 :

From (1) and (2), we get

a2 + b2  =  c2

4. Answer :

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. 

c2  =  412

c2  =  1681 -----(2)

Step 5 :

From (1) and (2), we get

a2 + b2  =  c2

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