Page 87 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\03_Chapter_3\Chapter_3
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

6. In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

A H G F
30°
110° x
x A
B C D E

E B
7. ABCDE is a regular pentagon as shown alongside. The bisector of angle A meets
the side CD at M. Find ∠AMC.
D M C
8. The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1 : 2. Can
it be a parallelogram? Why or why not?
9. A playground in the town is in the form of a kite. The perimeter is 106 metres. If one of its sides is
23 metres, what are the lengths of other three sides?

10. Construct a parallelogram ABCD such that AC = 10 cm; BD = 6.4 cm and an angle between them is 60°.
11. During picnic in the fun park, twins Reena and Sheena and their
parents are enjoying cold drink to beat the heat. They want to
relish their taste-buds for longer period, so they asked shopkeeper
for straws. He gave them four straws of lengths 11 cm, 11 cm, Case study
8 cm, 8 cm. Long straws for parents and short one for the young
twins, Reena and Sheena. The twins are constructing quadrilaterals
using these straws.
Based on the above information answer the following questions:
(a) How many types of quadrilaterals they can form using these straws?
(b) If Reena construct a quadrilateral ‘COLD’, such that OC = DL = 11 cm and CD = OL = 8 cm.
Also ∠C = ∠L and ∠O = ∠D. Then, which type of quadrilateral is the ‘COLD’?
(c) If Sheena construct a quadrilateral, ‘SNOW’, such that SN = NO = 11 cm and SW = WO =
8 cm. Also ∠S = ∠O and ∠N = ∠W, then which type of quadrilateral is the ‘SNOW’?

www
MAths connect

Rangoli is an art form in India. It is a type of decoration drawn on the ground or sidewalk in front
of a house. It consists of making geometric designs on the floor using coloured sand, petals, flour, or even rice.
A Rangoli has been drawn on a floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the
radius of semicircles drawn on each side of rhombus ABCD.

85