In maths, Geometry is a very interesting topic. Teach your child about different types of triangles with examples. Learn how to solve the problems and understand the concept of triangles and their properties. Students will find the basic geometric formulas for triangles from this page. Test yourself by solving the questions given in the properties of the triangle worksheet. Solving the worksheets will help the 5th grade math students to enhance their knowledge and also to score the highest marks in the exams.
Also, Refer:
Properties of Triangle Worksheet
Check out the properties of the triangles worksheet answer key from below.
Example 1.
The angles of a triangle are 40 degrees, 80 degrees, and 60 degrees. Is it is possible to construct a triangle?
Solution:
Given,
The angles of a triangle are 40 degrees, 80 degrees, and 60 degrees.
We know that
Sum of the angles of a triangle = 180 degrees
The length of the given angle = 60 + 80 + 40 = 180 degrees.
So, it is possible to construct a triangle.
Example 2.
The angles of a triangle are 70 degrees, 30 degrees, and 90 degrees. Is it is possible to construct a triangle?
Solution:
Sum of the angles of a triangle = 180 degrees
The length of the given angle = 70 + 40 + 90 = 200 degrees.
The length of the given angles is greater than the sum of the angles.
So, it is not possible to construct a triangle.
Example 3.
Measures of two angles of a triangle are 30 degrees and 60 degrees find the measure of its third angle?
Solution:
The measures of two angles of a triangle are 60degrees and 30 degrees.
Sum of the measures of two angles = 60 degrees + 30 degrees
Sum of all these angles of a triangle = 180 degrees.
Therefore, measure of the third angle = 180 degrees – 90 degrees = 90degrees
Example 4.
The lengths of sides are 2cm, 2cm, and 6cm and that is the triangle?
Solution:
The length of the sides is 2cm, 2cm, and 6cm.
Here the sides of the triangle are equal and one side is different.
So it is an isosceles triangle.
Example 5.
The lengths of sides are 3cm, 3cm, and 3cm and that is the triangle?
Solution:
The length of the sides is 3cm, 3cm, and 3cm.
Here all the sides of the triangle are equal.
So it is an equilateral triangle.
Example 6.
The sum of the measures of three angles of a triangle is?
Solution:
The sum of the measures three angles of a triangle are 180°.
Example 7.
A triangle with unequal sides is called as?
Solution:
In a triangle all sides are not equal then it is a scalene triangle.
Example 8.
In the right angle, one angle is 30 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 = 30 degrees
Therefore ∆PQR = 180 degrees – (triangle Q + triangle P )
180 degrees – (90 degrees + 30 degrees)
180 degrees – 120 degrees
Triangle R = 60°.
Example 9.
The two sides of a given triangle are 6 units and 5 units its semi parameter is 12 units what is its area?
Solution:
Given,
The two sides of a given triangle are 6 units and 5 units it’s semi parameter is 12 units.
The two sides of a given triangle are
a= 6; b = 5
It’s semi parameter is ,S = 12
We know that,
2s = a + b + c
2(12) = 6 + 5+ c
24 = 11c
C = 2.18
Thus the third side of the triangle is 2.18 units.
Example 10.
If a : b : c is 1 : 2 : 3 and S = 26 find the area of the triangle ?
Solution:
Here a : b : c = 1 : 2 : 3
Let us assume a = 1x , b = 2x, c= 3x
Therefore a + b + c = 1x + 2x + 3x = 6x
a + b + c = 2s
2s = 6x
X = 3
Therefore the length of three sides are 1× 3 = 3 inches, 2 × 3 = 6 inches and 3 × 33 = 9 inches
The area of the triangle ∆ ABC is
√ (s (s – a)(s – a)(s – a))
√ 26(26 – 3)(26 – 6)( 26 – 9))
√203320 inches.