NCERT Solution For Class 10, Maths, Chapter 6 Triangles, Exercise 6.4

NCERT Solution For Class 10, Maths, Chapter 6 Triangles, Exercise 6.4

NCERT Solution For Class 10, Maths, Chapter 6 Triangles, Exercise 6.4 involves basics of triangles. this exercise 6.4 has total nine questions to study which are given below.

Class 10, Maths, Chapter 6, Exercise 6.4 Solutions

Q.1. Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm^{2} and 121 cm^{2}. If EF = 15.4 cm, find BC.

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Q.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.

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Q.3. In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that $\frac{ar\,\,(ABC)}{ar\,\,(DBC)}=\frac{AO}{DO}$

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Q.4. If the areas of two similar triangles are equal, prove that they are congruent.

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Q.5. D, E and F are respectively the mid-points of sides AB, BC and CA of Δ ABC. Find the ratio of the areas of Δ DEF and Δ ABC.

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Q.6. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

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Q.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.

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Tick the correct answer and justify :

Q.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

Ans:(C) correct answer. (See below)

Answer

Q.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

Ans:(D) is the correct answer.

Answer

Justification: Since the ratio of the areas of two similar triangles equal to the ratio of the squares of any two corresponding sides. Therefore

Ratio of areas = (4)^{2}: (9)^{2} = 16 : 81

∴(D) is the correct answer.

Class 10 , Maths, Chapter 6, Triangles (All exercise)