# CONVERSE OF THE PYTHAGOREAN THEOREM WORKSHEET

## About "Converse of the Pythagorean theorem worksheet"

Converse of the pythagorean theorem worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on right triangles.

## Converse of the Pythagorean theorem The Pythagorean Theorem states that if a triangle is a right triangle, then, the sum of the squares of the lengths of the  legs is equal to the square of the length of the hypotenuse.

That is, if a and b are legs and c is the hypotenuse, then

a² + b²  =  c²

The converse of the Pythagorean Theorem states that if a² + b²  =  c², then the triangle is a right triangle.

## Converse of the Pythagorean theorem worksheet - Problems

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

1)  9 inches, 40 inches, and 41 inches

2)  8 meters, 10 meters, and 12 meters

3)  14 cm, 23 cm, and 25 cm

4)  27 ft, 36 ft and 45 ft ## Converse of the Pythagorean theorem worksheet - Solution

Problem 1 :

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

9 inches, 40 inches, and 41 inches

Solution :

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

=  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.

Problem 2 :

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

8 meters, 10 meters, and 12 meters

Solution :

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

=  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.

Problem 3 :

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

14 cm, 23 cm, and 25 cm

Solution :

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

=  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.

Problem 4 :

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

27 ft, 36 ft and 45 ft

Solution :

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

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

Apart from the stuff given above, if you want to know more about "Converse of the pythagorean theorem", please click here

Apart from the stuff given on "Converse of the pythagorean theorem worksheet", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments... WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6