# Theory of Parallel lines and Basic proportionality theorem

## Practice Questions:

1. In triangle PQR, a line segment PC divides QR in the ratio of 3 :5,

a) find the ratio of areas of triangles PQC and PQR.

b) find the ratio of areas of triangles PQC and PCR.

2. In triangle ABC, points D and E are on line segment BC such that BD : DE : EC = 3:2:1. Also F is a point on line segment AC such that AF : FC = 1: 1.

a) Find the ratio of areas of triangles ABD and ABC.

b) Find the ratio of areas of triangle FEC and ABC.

c) Find the ratio of areas of triangle FEC and ABD.

d) Find the ratio of areas of triangles ACD and FEC.

e) If the area of triangle ABC is given as 120 square units, find the area of quadrilateral ADEF.

3. If line segments PQ and RS intersect at O such that PO : OQ = 5 : 6 and RO : OS = 4: 3. Find the ratio of areas of triangles POR and SOQ.

4. In a triangle ABC, points P, Q and R are on sides AB, BC and AC respectively such that AP : PB = 3: 2, BQ : QC = 1:1, AR : RC = 4 : 3.

a) Find the ratio of areas of triangles PQR and ABC.

b) Find the ratio of areas of triangles PBQ and PQR.

c) Find the ratio of areas of triangles PQR and RQC.

## Answers

- A) 3 : 8 b) 3 : 5 2. A) 1 : 2 b) 1 : 12 c) 1 : 6 d) 6 : 1 e) 50

3. 10 : 9 4. A) 17 : 70 b) 14 : 17 c) 17 : 15

1.(a)3:8

(b)3:5

2.(a)1:2

(b)1:12

(c)

(d)6:1

(e)

3.10:9

4.(a)17:70

(b)14:17

(c)17:15

1.(A)-3:8

(B)-3:5

2.(A)-1:2

(B)-1:12

(C)-1:6

(D)-6:1

(E)-50 sq. units

3.10:9

1.(a) 3:8

(b) 3:5

2.(a)1:2

(b) 1:12

(c)

(d)6:1

(e)

3.10:9

4.(a)17:70

(b)14:17

(c)17:15

completed!1

Done