Construct a quadrilateral LION with LI=6.5 cm, IO=7.2 cm, Angle I=90°, Angle O=60° and Angle N=105°.
Answers
Answer:
Step-by-step explanation:
Step 5: Join AC as a dotted line. Step 7: With C as centre and radius 5 cm, draw an
arc intersecting the previous arc at D. Join
X
X C CD and AD.
C D X
3.8 cm 5cm X C
90° 3.8 cm C
A 90° B 6cm 3.8 cm
A 4.5 cm B 90° 3.8 cm
4.5 cm
A 90° B
4.5 cm
Fig. 4.6 (e) A B
4.5 cm
Step 6: With A as centre and radius 6 cm, draw an Fig. 4.6 (f)
arc on the side opposite to B. Thus, ABCD is the required quadrilateral
Exercise 4.2
1. Construct a quadrilateral ABCD where AB = 5.5 cm, BC = 6.5 cm, CD = 7 cm, ∠ABC = 120° and
∠BCD = 90°.
2. Construct a quadrilateral FEAR , where FE = 4.1 cm, EA = 5.6 cm, AR = 4 cm, ∠A = 120° and
∠E = 75°.
3. Construct a quadrilateral ABCD with AB = 5.5 cm, AD = 6 cm, ∠A = 120° , ∠D = 90° and ∠B = 40°.
4. Construct a parallelogram PQRS, where PQ = 7 cm, QR = 5 cm, ∠P = 60° and ∠Q = 120°.
5. Construct a quadrilateral LION with LI = 6.5 cm, IO = 7.2 cm, ∠I = 90°, ∠O = 60° and ∠N = 105°.
CONSTRUCTION OF SOME SPECIAL Step 2: Draw a line segment AB = 5.2 cm.
TYPES OF QUADRILATERALS Step 3: With A as centre and radius 3.2 cm (half of
Special types of quadrilaterals can be constructed one diagonal), draw an arc.
and classified by relationships of their sides, angles Step 4: With B as centre and radius 3 cm (half of
and diagonals. Let us see the constructions of another diagonal), draw another arc, cutting
different types of quadrilaterals as given below. the previous arc at O.
Illustration 1: Let us construct a parallelogram with Step 5: Join OA and OB.
one side and both diagonals. We know that the Step 6: Produce AO to C such that OC = AO and
diagonals of a parallelogram bisect each other. produce BO to D such that OD = OB.
To construct a parallelogram, one of whose sides is Step 7: Join AD, BC and CD.
5.2 cm and diagonals are 6 cm and 6.4 cm, we follow
these steps: D C
Step 1: Draw a rough sketch of the required
parallelogram, as shown in Fig. 4.7(a).
3.2 cm
D C O 3 cm
3.2 cm A 5.2 cm B
3.0 cm
3.2 cm O 3.0 cm Fig. 4.7 (b)
Thus, ABCD is the required parallelogram.
A 5.2 cm B
Fig. 4.7 (a)
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