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.