Question

Name the type of triangles based on their (a) sides
(1)
 

(2)

(3)

(b) angles
(1)

(2)

(3)

(4)

Answer 1

Hint:
Here, in the given question, the data is given in the pictorial form. We have to analyse the data and check the type of the triangle according to their lengths of sides and angles. Thus, write the types of triangles based on the sides and angles.

Complete step by step solution:
Firstly, we need to verify the lengths of the sides of the given triangles.
(1)

Here, lengths of all the sides of the triangle are the same. So, the given triangle is an equilateral triangle.
(2)

Here, the lengths of the sides of the triangle are all different. So, the given triangle is a scalene triangle.
(3)

Here, the lengths of the two sides of the triangle are the same and the other one side has different lengths. So, the given triangle is an isosceles triangle.
Now, we need to verify the type of triangles with the help of the angles.
(1)

Here, one angle of the triangle exceeds 90. So, the given triangle is an obtuse triangle.
(2)

Here, all the angles of the triangle have same value and the values are lesser than 90. So, the given triangle is an acute triangle.
(3)

Here, one of the angles of the triangle is greater than 90. So, the given triangle is an obtuse triangle.
(4)

Here, one angle of the triangle is equal to 90 and the other two are 60 and 30. So, the given triangle is a right-angled triangle.

Note:
Equilateral triangle: In a triangle if lengths of all sides are equal, then that triangle is called equilateral triangle.
Isosceles triangle: In a triangle if lengths of two triangles are equal and the length of the other remaining side is different, then that triangle is called an isosceles triangle.
Scalene triangle: In a triangle if the lengths of all sides are different, then that triangle is called scalene triangle.
Obtuse triangle: In a triangle if one of the angles of the triangle exceeds 90, then that triangle is called an obtuse angled triangle.
Acute triangle: In a triangle if all of the angles of the triangle are less than 90, then that triangle is called an acute angled triangle.
Right triangle: in a triangle if one of the angles of the triangle is exactly 90 and sum of the other two angles is 90, then that triangle is called right-angled triangle.