Q. 34.5( 2 Votes )

Match the followi

Answer :

A. We have ratio of angles = 5:5:8


Observe that first two angles are equal. So, the triangle is isosceles. Now, we need to check if it is also right-angled.


To find that, let us assume the angles are 5x, 5x and 8x.


We know sum of angles in a triangle is 180°.


5x + 5x + 8x = 180°


18x = 180°



So, angles are 50°, 50° and 80° that is, it is not a right angled triangle.


Thus, 5:5:8 ISOSCELES triangle (option IV)


B. We have ratio of angles = 1:3:5


Let us assume the angles are x, 3x and 5x.


We know sum of angles in a triangle is 180°.


x + 3x + 5x = 180°


9x = 180°



So, angles are 20°, 60° and 100°.


One angle is greater than 90°. So, this triangle has an obtuse angle.


Thus, 1:3:5 OBTUSE-ANGLED triangle (option II)


C. We have ratio of angles = 1:1:1


This means all angles in the triangle are equal.


Thus, 1:1:1 EQUILATERAL triangle (option V)


D. We have ratio of angles = 1:2:3


Let us assume the angles are x, 2x and 3x.


We know sum of angles in a triangle is 180°.


x + 2x + 3x = 180°


6x = 180°



So, angles are 30°, 60° and 90°.


One angle is equal to 90°. So, this triangle has a right angle.


Thus, 1:2:3 RIGHT-ANGLED triangle (option I)


E. We have ratio of angles = 1:1:2


Observe that first two angles are equal. So, the triangle is isosceles. Now, we need to check if it is also right-angled.


To find that, let us assume the angles are x, x and 2x.


We know sum of angles in a triangle is 180°.


x + x + 2x = 180°


4x = 180°



So, angles are 45°, 45° and 90° that is; there is also a right angle in this triangle. This triangle is both right angled and isosceles.


Thus, 1:1:2 RIGHT-ANGLED ISOSCELES triangle (option III)


Hence, the answer is A – IV, B – II, C – V, D – I, E – III.



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
RELATED QUESTIONS :

In a right-angledNCERT - Exemplar Mathematics

In Fig. 6.34, finNCERT - Exemplar Mathematics

Find the values oNCERT - Exemplar Mathematics

In Δ ABC, if <spaNCERT - Exemplar Mathematics

In a triangle ABCNCERT - Exemplar Mathematics

In Fig. 6.31(i) aNCERT - Exemplar Mathematics

In Fig. 6.30, finNCERT - Exemplar Mathematics

The measure of thNCERT - Exemplar Mathematics