NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Exercise 6.1

Question 1:
Fill in the blanks using the correct word given in brackets :
(i) All circles are . (congruent, similar)
(ii) All squares are . (similar, congruent)
(iii) All triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are . (equal, proportional)

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Question 2:
Give two different examples of pair of
(i) similar figures. (ii) non-similar figures.

Question 3:
State whether the following quadrilaterals are similar or not:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Exercise 6.2

Question 1:
In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

Question 2:
E and F are points on the sides PQ and PR respectively of a  PQR. For each of the following cases, state whether EF || QR :
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

Question 3:
In Fig. 6.18, if LM || CB and LN || CD, prove that
\(\frac{AM}{AB}\) = \(\frac{AN}{AD}\).

Question 4:
In Fig. 6.19, DE || AC and DF || AE. Prove that
\(\frac{BF}{FE}\) = \(\frac{BE}{EC}\).

Question 5:
In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.

Question 6:
In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR.
Show that BC || QR.

Question 7:
Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Question 8:
Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

Question 9:
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

NCERT Solutions for Class 10 Maths Chapter 6