Question

Case study
Seema placed a lightbulb at point O om the ceiling and directly below it placed a

table. Now she put a cardboard of shape between table and lighted bulb.

Then a shadow of ABCD is casted on the table as A’B’C’D’ (see figure).

Quadrilateral A’B’C’D’ is an enlargement of ABCD with scale factor 1:2. Also,

AB= 15 cm, BC=25 cm, CD=24 cm and AD=21 cm; ∠ = 105°, ∠ = 100°, ∠ =

70° and ∠ = 85° .

a. What is the measurement of angle A’?

(i) 105° (ii) 100° (iii) 70° (iv) 80°

1

b. What is the length of A’B’?

(i)15 cm (ii) 30 cm (iii) 50 cm (iv) 25 cm

1

c. What is the sum of angles of quadrilateral A’B’C’D’?

(i) 180° (ii) 360° (iii) 270° (iv) None of these

1

d. What is the ratio of sides A’B’ and A’D’?

(i) 5:7 (ii) 7:5 (iii) 1:1 (iv) 1:2

1

e. What is the sum of angles of C’ and D’?

(i) 105° (ii) 100° (iii) 155° (iv) 140°​

Answer 1

Answer:

(a) A' is 105°

( as A is is 105°) --- bcz of corresponding angles

(b) A'B' is 30 cm

as ratio is divided in 1:2 , A'B' is double of AB(15cm) i.e 30 cm

(c) 360° ( as quadrilateral is always 360°)

(d) 5/7

A'B'C'D' is double of ABCD ( each side of A'B'C'D'is double of ABCD)

so 30/42 i.e 5/7

(e)155°

As all angles are equal bcz of corresponding angles

C'+D'= 70+85= 155°