Question

PRACTICAL GEOMETRY
1. Construct a quadrilateral XYZW in which XY = 4 cm, YZ = 4.5 cm, XZ = 60
WZ = 4 cm and XW = 5 cm. Write the steps of construction​

Answer 1

Step-by-step explanation:

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.