#### 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.

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