In the previous article, we have discussed the properties of the triangle in detail. Now we are going to discuss the examples of properties of triangles with a brief explanation from here. Know the types of triangles based on the sides and angles. So, we suggest the 5th-grade students know how to solve the problems on the triangle and their importance from this page.

**Do Refer:**

## Properties of a Triangle | Basic Triangle Properties

- A triangle has three sides, three angles, and three vertices.
- The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.
- The sum of the length of any two sides of a triangle is greater than the length of the third side.
- The side opposite to the largest angle of a triangle is the largest side.
- Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

### Examples of Properties of Triangle

Have a look at the examples given in the below section to know deeply about the properties of a triangle.

**Example 1.**

Measures of two angles of a triangle are 55 degrees and 45 degrees find the measure of its third angle?

**Solution:**

The measures of two angles of a triangle are 55 degrees and 45 degrees.

The sum of the measures of two angles = 55 degrees + 45 degrees

Sum of all these angles of a triangle = 180 degrees.

Therefore, the measure of the third angle = 180 degrees – 105 degrees = 75 degrees

**Example 2.**

The construction of a triangle is possible in which the lengths of sides are 3cm, 5cm, and 7cm?

**Solution:**

The length of the sides are 3cm, 5cm, and 7cm

Sum of the smallest two sides = 3cm + 5cm = 8cm

The third side length = 7cm

The sum of tho small sides is greater than the third side

So, it is possible to construct a triangle.

**Example 3.**

The construction of a triangle is possible in which the lengths of sides are 3cm, 3cm, and 3cm?

**Solution:**

The length of the sides are 3cm, 5cm, and 3cm

The length of the sides of a triangle is equal.

So, it is possible to construct a triangle.

It is an equilateral triangle.

Example 4.

The construction of a triangle is possible in which the lengths of sides are 3cm, 2cm, and 7cm?

Solution:

The length of the sides are 3cm, 2cm, and 7cm

Sum of the smallest two sides = 3cm +2cm = 5cm

The third side length = 7cm

The sum of the small sides is less than the third side

So, it is possible to construct a triangle.

**Example 5.**

In a right angle triangle if one angle is 40 degrees find its third angle?

**Solution:**

∆ PQR is a right angle triangle, that is one angle is a right angle.

Given that,

∆ PQR = 90 degrees

∆ PQR = 40 degrees

Therefore ∆PQR = 180 degrees – (triangle Q + triangle P )

180 degrees – (90 degrees + 40 degrees)

180 degrees – 130 degrees

Triangle R = 50 degrees

**Example 6.**

The two sides of a given triangle are 4 units and 6 units its semi parameter is 12 units what is its area?

**Solution:**

The two sides of a given triangle are

a= 4; b = 6

It’s semi parameter is ,S = 12

We know that,

2s = a + b + c

2(12) = 4 + 6 + c

24 = 10c

C = 2.4

Thus the third side of the triangle is 2.4 units

**Example 7.**

If a : b : c is 3 : 4 : 5 and S = 26 find the area of the triangle ?

**Solution:**

Here a : b : c = 3 : 4 : 5

Let us assume a = 3x , b = 4x, c= 5x

Therefore a + b + c = 3x + 4x + 5x = 12x

a + b + c = 2s

2s = 12x

X = 4.3

Therefore the length of three sides are 3× 4.3 = 12.9 inches, 4 × 4.3 = 17 2 inches and 5 × 4.3 = 21.5 inches

The area of the triangle ∆ ABC is

√ (s (s – a)(s – a)(s – a))

√ 26(26 – 12.9)(26 – 17.9)( 26 – 21.5))

√53951.04 inches.

**Example 8. **

The angle of a triangle is 40° and 30° what type of triangle it is?

**Solution:**

The triangle is the scalene and obtuse triangle.

**Example 9.**

Measures of two angles of a triangle are 40 degrees and 30 degrees find the measure of its third angle?

**Solution:**

The measures of two angles of a triangle are 40 degrees and 30 degrees.

The sum of the measures of two angles = 40 degrees + 30 degrees

The Sum of all these angles of a triangle = 180 degrees.

Therefore, measure of the third angle = 180 degrees – 70 degrees = 110degrees

**Example 10. **

The two sides of a given triangle are 2 units and 5 units it’s semi parameter is 10 units what is its area ?

**Solution:**

The two sides of a given triangle are

a= 2; b = 5

It’s semi parameter is ,S = 10

We know that,

2s = a + b + c

2(10) = 2 + 7 + c

20= 9c

C = 2.22

Make use of the article to know about the properties of triangles. Also go through the related articles in 5th-grade math where you can find examples, worksheets, practice questions, etc. Hence keep in touch with our page to get all the topics of basic maths and enhance your skills.