## EXERCISE 6.2

#### Page No 128:

#### Question 1:

In figure.6.17. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

(i)

(ii)

#### Answer:

(i)

Let EC = *x* cm

It is given that DE || BC.

By using basic proportionality theorem, we obtain

(ii)

Let AD = *x *cm

It is given that DE || BC.

By using basic proportionality theorem, we obtain

Video Solution

#### Question 2:

E and F are points on the sides PQ and PR respectively of a ΔPQR. 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 = 0.63 cm

#### Answer:

(i)

Given that, PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm, FR = 2.4 cm

(ii)

PE = 4 cm, QE = 4.5 cm, PF = 8 cm, RF = 9 cm

(iii)

PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm, PF = 0.36 cm

Video Solution

#### Question 3:

In the following figure, if LM || CB and LN || CD, prove that

#### Answer:

In the given figure, LM || CB

By using basic proportionality theorem, we obtain

#### Question 4:

In the following figure, DE || AC and DF || AE. Prove that

#### Answer:

In ΔABC, DE || AC

Video Solution

#### Page No 129:

#### Question 5:

In the following figure, DE || OQ and DF || OR, show that EF || QR.

#### Answer:

In Δ POQ, DE || OQ

Video Solution

#### Question 6:

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

#### Answer:

In Δ POQ, AB || PQ

Video Solution

#### Question 7:

Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

#### Answer:

Consider the given figure in which *l* is a line drawn through the mid-point P of line segment AB meeting AC at Q, such that .

Or, Q is the mid-point of AC.

Video Solution

#### Question 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).

#### Answer:

Consider the given figure in which PQ is a line segment joining the mid-points P and Q of line AB and AC respectively.

i.e., AP = PB and AQ = QC

It can be observed that

Hence, by using basic proportionality theorem, we obtain

Video Solution

#### Question 9:

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

#### Answer:

Draw a line EF through point O, such that

In ΔADC,

By using basic proportionality theorem, we obtain

In ΔABD,

So, by using basic proportionality theorem, we obtain

From equations (1) and (2), we obtain

Video Solution

#### Question 10:

The diagonals of a quadrilateral ABCD intersect each other at the point O such that** **Show that ABCD is a trapezium.

#### Answer:

Let us consider the following figure for the given question.

Draw a line OE || AB

In ΔABD, OE || AB

By using basic proportionality theorem, we obtain

However, it is given that

⇒ EO || DC [By the converse of basic proportionality theorem]

⇒ AB || OE || DC

⇒ AB || CD

∴ ABCD is a trapezium.