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Steps of construction:
From any ray AX, cut the line segment AB = a. At Aof the line segment AB,
construct the angle ‘BAY =‘x and at B, construct the angle ‘ABZ =‘y. From the
line segment AB, cut a line segment AE=b. Now at E, construct BC || AY which cuts
BZ at C. Now construct CD || BA. The line segment CD intersects the ray AY at D.
ThenABCD is the required trapezium.
Proof : By construction, AB || CD and AD || EC. Therefore, AECD is a parallelogram
andCD = AE = b. Now in the quadrilateral ABCD,AB=a,CD=b,AB || CD and
‘BAD =‘x,‘ABC =‘y (by construction). Therefore, ABCD is the required
trapezium.

Activity : The perimeter and an angle of a rhombus are given. Construct the

rhombus.

Exercise 7⋅ 2

1. The two angles of a right angled triangle are given. Which one of the following

combination allows constructing the triangle?

a. 63q and 36q b. 30q and 7 0 q c. 40q and 50q d. 8 0 q and 2 0 q

2. i. A rectangle is a parallelogram

ii. A square is a rectangle

iii. A rhombus is a square

On the basis of the above information, which one of the following is true?

a. i and ii b. i and iii c. ii and iii d. i, ii and iii

In view of the given figure, answer the questions 3 and 4.

3. What is the area of 'AOB?
   a. 6 sq. units b. 7 sq. units c. 12 sq. units d.14 sq. units


4. The perimeter of the quadrilateral is
   a. 12 units b. 14 units c. 20 units d. 28 units


5. Construct a quadrilateral with the following data :
   (a) The lengths of four sides are 3 cm, 3˜5 cm, 2.5 cm, 3cm and an angle is 45q.
   (b) The lengths of four sides are 3.5 cm, 4 cm, 2˜5 cm 3.5 cm and a diagonal is 5 cm.
   (c) The lengths of three sides are 3 ˜ 2 cm, 3 cm, 3˜5 cm and two diagonals are
   2 ˜ 8 cm, and 4.5 cm.