NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

These NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.4

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

Question 1.
Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm² and 121 cm². If EF = 15.4 cm, find BC.
Solution:
Since, ∆ABC ~ ∆DEF
The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 1

Question 2.
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.
Solution:
ABCD is a trapezium with AB || DC and AB = 2 CD
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 2

Question 3.
In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 2a
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 3
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 4

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

Question 4.
If the areas of two similar triangles are equal, prove that they are congruent.
Solution:
Given : Areas of two similar triangles are equal.
To Prove : Triangles are congruent. Ratio in the areas of two similar triangles is equal to the ratio of their respective sides.
Proof: Let ∆ABC and ∆PQR be two triangles.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 5
Hence, by SSS congruence theorem
∆ ABC ≅ ∆PQR (Proved)

Question 5.
D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ABC. Find the ratio of the areas of ∆DEF and ∆ABC.
Solution:
ABC is a triangle and D, E, F are the mid¬points of the sides AB, BC and CA respectively
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 6

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

Question 6.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Solution:
Given ∆ ABC ~ ∆DEF, and AP and DQ are their medians.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 7

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

Question 7.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
Solution:
Given A square ABCD. Equilateral ABCE and AACF have been described on side BC diagonal AC respectively.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4 8

Question 8.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is _________.
(a) 2 : 1
(b) 1 : 2
(c) 4 : 1
(d) 1 : 4
Solution:
(c) 4 : 1

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.4

Question 9.
Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio __________.
(a) 2 : 3
(b) 4 : 9
(c) 81 : 16
(d) 16 : 81
Solution:
(d) 16 : 81

error: Content is protected !!