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Ncert Solutions for Class 10

Triangles

Triangles

Exercise 6.1

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)

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

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

               

Triangles

Exercise 6.2

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

 

2. E and F are points on the sides PQ and PR respectively of a ΔPQR. State whether EF || QR, if:
(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.

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

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

5. In Figure, DE || OQ and DF || OR. Show that EF || QR.

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

7. Using Basic Proportionality Theorem, 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).

8. Using Converse of Basic Proportionality Theorem, 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).

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

10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that \(\frac{AO}{BO}=\frac{CO}{DO}\)⋅