CONVERSE OF THE PYTHAGOREAN THEOREM WORKSHEET

Problem 1 :

Determine whether triangle with the side lengths given below is a right triangle.

9 inches, 40 inches, and 41 inches

Problem 2 :

Determine whether triangle with the side lengths given below is a right triangle.

8 meters, 10 meters, and 12 meters

Problem 3 :

Determine whether triangle with the side lengths given below is a right triangle.

14 cm, 23 cm, and 25 cm

Problem 4 :

Determine whether triangle with the side lengths given below is a right triangle.

27 ft, 36 ft and 45 ft

Answers

1. Answer :

9 inches, 40 inches, and 41 inches

Step 1 :

Let a = 9, b = 40, and c = 41.

(Always assume the longest side as "c")

Step 2 :

Find the value of (a² + b²). 

a² + b²  =  9² + 40²

a² + b²  =  81 + 1600

a² + b²  =  1681 ----- (1)

Step 3 :

Find the value of c². 

c²  =  41²

c²  =  1681 ----- (2)

Step 4 :

From (1) and (2), we get

a² + b²  =  c²

By the converse of Pythagorean theorem, the triangle with the side lengths 9 inches, 40 inches, and 41 inches is a right triangle. 

2. Answer :

8 meters, 10 meters, and 12 meters

Step 1 :

Let a = 8, b = 10, and c = 12.

(Always assume the longest side as "c")

Step 2 :

Find the value of (a² + b²). 

a² + b²  =  8² + 10²

a² + b²  =  64 + 100

a² + b²  =  164 ----- (1)

Step 3 :

Find the value of c². 

c²  =  12²

c²  =  144 ----- (2)

Step 4 :

From (1) and (2), we get

a² + b²  ≠  c²

By the converse of Pythagorean theorem, the triangle with the side lengths 8 meters, 10 meters, and 12 meters is not a right triangle. 

3. Answer :

14 cm, 23 cm, and 25 cm

Step 1 :

Let a = 14, b = 23, and c = 25.

(Always assume the longest side as "c")

Step 2 :

Find the value of (a² + b²). 

a² + b²  =  14² + 23²

a² + b²  =  196 + 529

a² + b²  =  725 ----- (1)

Step 3 :

Find the value of c². 

c²  =  25²

c²  =  625 ----- (2)

Step 4 :

From (1) and (2), we get

a² + b²  ≠  c²

By the converse of Pythagorean theorem, the triangle with the side lengths 14 cm, 23 cm, and 25 cm is not a right triangle. 

4. Answer :

27 ft, 36 ft and 45 ft

Step 1 :

Let a = 27, b = 36, and c = 45.

(Always assume the longest side as "c")

Step 2 :

Find the value of (a² + b²). 

a² + b²  =  27² + 36²

a² + b²  =  729 + 1296

a² + b²  =  2025 -----(1)

Step 3 :

Find the value of c². 

c²  =  45²

c²  =  2025 -----(2)

Step 4 :

From (1) and (2), we get

a² + b²  =  c²

By the converse of Pythagorean theorem, the triangle with the side lengths 27 ft, 36 ft and 45 ft is a right triangle.

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