 # Examples of Properties of Triangle | Properties of Triangle Problems with Solutions

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.

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## 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.

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