# PROPERTIES OF TRIANGLE WORKSHEET

## About "Properties of triangle worksheet"

Properties of triangle worksheet is much useful to the students who would like to practice problems on triangles.

Before we look at the worksheet, let us come to know the properties of the triangle.

The following are the two important properties of triangle.

1. The sum of the lengths of any two sides of a triangle is greater than the third side.

2. The sum of all the three angles of a triangle is 180°.

## Some other properties of triangle

1.  In an equilateral triangle, all the three sides and three angles will be equal and each angle will measure 60°.

2. In an isosceles triangle, the lengths of two of the sides will be equal. And the corresponding angles of the equal sides will be equal.

2.  In a right triangle, square of the hypotenuse is equal to the sum of the squares of other two sides. This is known as Pythagorean theorem.

Hypotenuse : The longest side of in the right triangle which is opposite to  right angle (90°)

## Properties of triangle worksheet - Problems

1)   Is it possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm ?

2)   Is it possible to have a triangle whose sides are 7 cm, 2 cm and 4 cm ?

3)   Find the length of the hypotenuse of the right triangle where the lengths of the other two sides are 8 units and 6 units.

4)   The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.

5)   The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right angle triangle is formed. Find the length of each side of the equilateral triangle.

6)   Can 30°, 60° and 90° be the angles of a triangle ?

7)   Can 35°, 55° and 95° be the angles of a triangle ?

8)   In a triangle, If the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle.

9)   If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

10)   In a triangle, If the second angle is 10% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

11)   If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

12)   In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

13)   In a right triangle, apart from the right angle, the other two angles are x+1 and 2x+5. Find the angles of the triangle.

14)   In a triangle, if the second angle is 3 times the sum of the first angle and 3 and the third angle is the sum of 2 times the first angle and 6, find the three angles of the triangle.

15)   In a triangle, the ratio between the first and second angle is 1 : 2 and the third angle is 72. Find the first and second angle of the triangle.

## Properties of triangle worksheet - Answers

Problem 1 :

Is it possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm ?

Solution :

According to the properties of triangle explained above, if the sum of the lengths of any two sides is greater than the third side, then the given sides will form a triangle.

Let us apply this property for the given sides.

5 cm + 6 cm > 4 cm.

6 cm + 4 cm > 5 cm.

5 cm + 4 cm > 6 cm

Since the given sides meet the condition said in the property, It is possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 2 :

Is it possible to have a triangle whose sides are 7 cm, 2 cm and 4 cm ?

Solution :

According to the properties of triangle explained above, if the sum of the lengths of any two sides is greater than the third side, then the given sides will form a triangle.

Let us apply this property for the given sides.

2 cm  + 4 cm  <  7 cm.

From the above point, it is clear the sum of the lengths of the two sides 2 cm and 4 cm is  less than the third side 7 cm.

Since the given sides do not meet the condition said in the property,

Hence, it is not possible to have a triangle whose sides are 7 cm, 2 cm and 4 cm.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 3 :

Find the length of the hypotenuse of the right triangle where the lengths of the other two sides are 8 units and 6 units.

Solution :

From the given information we can draw the triangle as given below.

In the above triangle, we have to find the value of "x"

According to Pythagorean theorem, square of the hypotenuse is equal to the sum of the squares of other two sides

So, we have

x²  =  8² + 6²

x²  =  64 + 36

x²  =  100

x  =  10

Hence, the length of the hypotenuse is 10 units.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 4 :

The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.

Solution :

Let "x" and "x+4" be the lengths of other two sides.

Using Pythagorean theorem, (x+4)² + x²  =  202

x² + 8x + 16 + x² - 400  =  0

2x² + 8x - 384  =  0

x² + 4x - 192  =  0

(x+16)(x-12)  =  0

x  =  -16 or x  =  12

x = -16 can not be accepted. Because length can not be negative.

If x  =  12,

x + 4  =  12 + 4  =  16

Hence, the other two sides of the triangle are 12 cm and 16 cm.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 5 :

The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right angle triangle is formed. Find the length of each side of the equilateral triangle.

Solution :

Let "x" be the length of each side of the equilateral triangle.

Then, the sides of the right angle triangle are (x-12), (x-13) and             (x-14)

In the above three sides, the side represented by (x -12) is hypotenuse (because that is the longest side).

Using Pythagorean theorem, (x-12)²  =  (x-13)² + (x-14)2

x² - 24x + 144  =  x² - 26x + 169 + x² - 28x + 196

x² - 30x + 221  =  0

(x - 13)(x - 17)  =  0

x  =  13  or  x  =  17.

x  =  13 can not be accepted. Because, if x  =  13, one of the sides of the right angle triangle would be negative.

Hence, the side of the equilateral triangle is 17 units.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 6 :

Can 30°, 60° and 90° be the angles of a triangle ?

Solution :

Let us add all the three given angles and check whether the sum is equal to 180°.

30° +  60° + 90°  =  180°

Since the sum of the angles is equal 180°, the given three angles can be the angles of a triangle.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 7 :

Can 35°, 55° and 95° be the angles of a triangle ?

Solution :

Let us add all the three given angles and check whether the sum is equal to 180°.

35° +  55° + 95°  =  185°

Since the sum of the angles is not equal 180°, the given three angles can not be the angles of a triangle.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 8 :

In a triangle, If the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle.

Solution :

Let "x" be the first angle.

The second angle  =  x + 5

The third angle  =  x + 5 + 5  =  x + 10

We know that,

the sum of the three angles of a triangle  =  180°

x + (x+5) + (x+10)  =  180°

3x + 15  =  180

3x  =  165

x  =  55

The first angle  =  55°

The second angle  =  55 + 5  =  60°

The third angle  =  60 + 5  =  65°

Hence, the three angles of a triangle are 55°, 60° and 65°.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 9 :

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

Solution :

From the ratio 2 : 7 : 11,

the three angles are 2x, 7x, 11x

In any triangle, sum of the angles = 180°

So, 2x + 7x + 11x  =  180°

20x  =  180 -------> x  =  9

Then, the first angle  =  2x  =  2(9)  = 18°

The second angle  =  7x  =  7(9)  =  63°

The third angle  =  11x  =  11(9)  99°

Hence the angles of the triangle are (18°, 63°, 99°)

Let us look at the next problem on "Properties of triangle worksheet"

Problem 10 :

In a triangle, if the second angle is 10% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

Solution :

Let "x" be the first angle.

The second angle  =  120 % of x  =  1.2x

The third angle  =  80% of x  =  0.8x

We know that,

the sum of the three angles of a triangle  =  180°

x + 1.2x + 0.8x  =  180°

3x  =  180°

x  =  60°

The first angle  =  60°

The second angle  =  1.2(60)  =  72°

The third angle  =  0.8(60)  =  48°

Hence, the three angles of a triangle are 60°, 72° and 48°.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 11 :

If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

Solution :

Let "x" be the first angle.

The second angle  =  x + 1

The third angle  =  x + 1 + 1  =  x + 2

We know that,

the sum of the three angles of a triangle  =  180°

x + x + 1 + x + 2  =  180°

3x + 3  =  180°

3x  =  177°

x  =  59°

The first angle  =  59°

The second angle  =  59 + 1  =  60°

The third angle  =  60 + 1  =  61°

Hence, the three angles of a triangle are 59°, 60° and 61°.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 12 :

In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

Solution :

Let "x" be the first angle.

The second angle  =  2x

The third angle  =  3x

We know that,

the sum of the three angles of a triangle  =  180°

x + 2x + 3x  =  180°

6x  =  180°

x  =  30°

The first angle  =  30°

The second angle  =  2(30°)  =  60°

The third angle  =  3(30°)  =  90°

Hence, the three angles of a triangle are 30°, 60° and 90°.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 13 :

In a right triangle, apart from the right angle, the other two angles are x+1 and 2x+5. find the angles of the triangle.

Solution :

We know that,

the sum of the three angles of a triangle  =  180°

90 + (x + 1) + (2x + 5)  =  180°

3x + 6  =  90°

3x  =  84°

x  =  28°

So,  x + 1  =  28 + 1  =  29°

2x + 5  =  2(28) + 5  =  56 + 5  =  61°

Hence, the three angles of a triangle are 90°, 29° and 61°.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 14 :

In a triangle, if the second angle is 3 times the sum of the first angle and 3 and the third angle is the sum of 2 times the first angle and 3, find the three angles of the triangle.

Solution :

Let "x" be the first angle.

The second angle  =  3(x+3)

The third angle  =  2x + 3

We know that,

the sum of the three angles of a triangle  =  180°

x + 3(x+3) + 2x + 3  =  180°

x + 3x + 9 + 2x + 3  =  180°

6x + 12  =  180°

6x  =  168°

x  =  28°

The first angle  =  28°

The second angle  =  3(28+3)  =  93°

The third angle  =  2(28) + 3  =  59°

Hence, the three angles of a triangle are 28°, 93° and 59°.

Let us look at the next problem on "Properties of triangle worksheet"

Problem 15 :

In a triangle, the ratio between the first and second angle is 1 : 2 and the third angle is 72. Find the first and second angle of the triangle.

Solution :

From the given ratio,

The first angle  =  x

The second angle  =  2x

We know that,

the sum of the three angles of a triangle  =  180°

x + 2x + 72  =  180°

3x  =  108°

x  =  36°

The first angle  =  36°

The second angle  =  2(36°)  =  72°

Hence, the first angle is  36° and the second angle is 72°.

After having gone through the stuff given above, we hope that the students would have understood "Properties of triangle worksheet".

If you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear 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