Question

Construct the following quadrilaterals of given measures.
(1) In ☐ MORE, l(MO) = 5.8 cm, l(OR) = 4.4 cm, m∠M = 58$°$, m∠O = 105$°$, m∠R = 90$°$.
(2) Construct ☐ DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm.
(3) In ☐ ABCD l(AB) = 6.4 cm, l(BC) = 4.8 cm, m∠A = 70$°$, m∠B = 50$°$, m∠C = 140$°$.
(4) Construct ☐ LMNO such that l(LM) = l(LO) = 6 cm, l(ON) = l(NM) = 4.5 cm, l(OM) = 7.5 cm.

Answer 1

(1)
Steps of Construction:

Step 1: Draw MO = 5.8 cm.

Step 2: Draw ∠MOX = 105$°$.

Step 3: With O as centre and radius 4.4 cm, draw an arc cutting ray OX at R.

Step 4: Draw ∠ORY = 90$°$.

Step 5: Draw ∠OMZ = 58$°$ such that ray MZ and ray RY intersect each other at E.



Here, MORE is the required quadrilateral.

(2)
Steps of Construction:

Step 1: Draw DE = 4.5 cm.

Step 2: With D as centre and radius 7.2 cm, draw an arc.

Step 3: With E as centre and radius 6.5 cm, draw an arc cutting the previous arc at F.

Step 4: Join EF.

Step 5: With D as centre and radius 5.5 cm, draw an arc.

Step 6: With E as centre and radius 7.8 cm, draw an arc cutting the previous arc at G.

Step 7: Join DG and GF.



Here, DEFG is the required quadrilateral.

(3)
Steps of Construction:

Step 1: Draw AB = 6.4 cm.

Step 2: Draw ∠ABX = 50$°$.

Step 3: With B as centre and radius 4.8 cm, draw an arc cutting ray BX at C.

Step 4: Draw ∠BCY = 140$°$.

Step 5: Draw ∠BAZ = 70$°$ such that ray AZ and ray CY intersect each other at D.



Here, ABCD is the required quadrilateral.

(4)
Steps of Construction:

Step 1: Draw LM = 6 cm.

Step 2: With L as centre and radius 6 cm, draw an arc.

Step 3: With M as centre and radius 7.5 cm, draw an arc cutting the previous arc at O.

Step 4: Join OL.

Step 5: With O as centre and radius 4.5 cm, draw an arc.

Step 6: With M as centre and radius 4.5 cm, draw an arc cutting the previous arc at N.

Step 7: Join ON and MN.



Here, LMNO is the required quadrilateral.