CLASS 10 MATH NCERT SOLUTIONS FOR CHAPTER – 6 TRIANGLES EX – 6.6

Triangles

Question 1.
In the given figure, PS is the bisector of ∠QPR of ∆PQR. Prove that 

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 90


Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 91

Question 2.
In the given figure, D is a point on hypotenuse AC of ∆ABC, DM ⊥ BC, and DN ⊥ AB. Prove that:

(i) DM2 = DN X MC
(ii) DN2 = DM X AN

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 92


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 93
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 94

Question 3.
In the given figure, ABc is triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2  + 2BC X BD

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 96


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 97

Question 4.
In the given figure, ABC is a triangle in which ∠ABC 90° and AD ⊥ CB. Prove that AC2 = AB2 + BC2 – 2BC X BD

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 98

Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 99

Question 5.
In the given figure, Ad is a median of a triangle ABC and AM ⊥ BC. Prove that
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 100

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 101
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 102
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 103

Question 6.
Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.Solution:

Solutions :-

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 99

Question 7.
In the given figure, two chords AB and CD intersect each other at the point P. Prove that:

(i) ∆APC ~∆DPB
(ii)
 AP X PB = CP X DP
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 105
Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 106

Question 8.
In the given figure, two chords Ab and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that:

(i) ∆PAC ~ ∆PDB
(ii)
PA X PB = PC X PD

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 107


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 108


Question 9.
In the given figure, D is a point on side BC of ∆ABC, such that  Prove that AD is the bisector of ∆BAC.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 109


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 110

Question 10.
Nazima is fly fishing in a stream. The trip of her fishing rod is 1.8m above the surface of the water and the fly at the end of the string rests on the water 3.6m away and 2.4 m from a point directly under the trip of the rod. Assuming that her string (from the trip of the rod to the fly) is that, how much string does she have out (see the figure)? If the pills in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 111

Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 112

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