Important Questions for CBSE Class 10 Maths Chapter 6 - Triangles 2 Mark Question


CBSE Class 10 Maths Chapter-6 Triangles – Free PDF Download

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CBSE Class 10 Maths Chapter-6 Triangles Important Questions

CBSE Class 10 Maths Important Questions Chapter 6 – Triangles


2 Mark Questions

1. In the given figures,and Find

(i) 
(ii) 
(iii) 
(iv) 
(v) 
Ans. (i) 
(ii) 

(iii) 
(iv)
(v) 


2. and their areas are respectively 64 cmand 121 cm2. If EF = 15.4 cm, find BC.

Ans. 

[the ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides]

=11.2 cm


3. ABC is an isosceles right triangle right-angled at C. Prove that 

Ans. In right-angled 
 [By Pythagoras theorem]


4. In the figure, DE||AC and , prove that

Ans. In 
[By Thales’s Theorem]
Also 
from (i) and (ii), we get
 [By the converse of Thales’s Theorem]


5. The hypotenuse of a right triangle is 6 m more than the twice of the shortest side. If the third side is 2m less than the hypotenuse. Find the side of the triangle.
Ans. Let shortest side be  in length
Then hypotenuse 
And third side = 
We have,


Hence, the sides of triangle are 10 m, 26 m and 24 m.


6. PQR is a right triangle right angled at P and M is a point on QR such that PMQR. Show that 
Ans. is a right triangle right angled at P and 


i. e.,


7. In the given figure, and Prove that 

Ans. In 

In 

From (i) and (ii), we get

From 


8. In figure, DE||BC, Find EC.
Ans. 



9. In the given figure, ABC and AMP are two right-angled triangles, right angled at B and M respectively, prove that


Ans. In and DAMP,
(Each )

are equiangular
i.e.,


10. In the given figure, OA × OB=OC × OD or prove that and 

Ans. In and 


And [Vertically opposite Angles]

[Corresponding angles of similar ]


11. In the given figure, DE||BC and AD=1 cm, BD = 2 cm. What is the ratio of the area of to the area of 
Ans. in

Also 


Hence, 


12. A right-angle triangle has hypotenuse of length p cm and one side of length q cm. If p – q =1, Find the length of third side of the triangle.

Ans. Let third side = x cm
Then by Pythagoras theorem,


13. The length of the diagonals of a rhombus are 24 cm and 10 cm. Find each side of rhombus.
Ans. 


From right-angled

Hence each side = 13 cm


14. In an isosceles right-angled triangle, prove that hypotenuse is times the side of a triangle.
Ans. Let hypotenuse of right-angledand equal sides of 
By Pythagoras theorem,


15. In figure, express x in terms of a, b, c.
Ans. 


16. The perimeter of two similar triangle ABC and PQR are respectively 36 cm and 24 cm. If PQ=10 cm, find AB.

Ans. 


17. In the given figure, DE||BC. If find the value of 

Ans. In the given figure,


18. The hypotenuse of a right-angled triangle is p cm and one of sides is q cm. if p = q+1, find the third side in terms of q.
Ans. Let third side be 

From (i) and (ii), we get


19. In the given figure,and AB = 5 cm, find the value of DC.

Ans. In and 
 [Vertically opposite angles]
 [Given]
 [By SAS similarity]


20. In and D is a point on side AC, such that . Prove that BD = BC.

Ans. Given: Ain which AB = AC, D is a point on BC
To prove: BD = BC
Proof:  [given]

In and 
and
[SAS similarity]