Practical Geometry

Mathematics

Mathematics

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First of all make a rough sketch. Do not start construction without drawing a rough sketch showing sides, angles and diagonals, etc., with correct name.

Step I. Draw a rough sketch and mark the measurements.

Step II. Draw AC = 7 cm.

Step III. With A as centre and radius 4 cm, draw an arc above AC.

Step IV. With C as centre and radius 6 cm, draw another arc intersecting the previous arc at B.

Step V. With centre A and radius 5.5 cm, draw an arc below AC.

Step VI. With centre C and radius 5 cm, draw another arc to intersect the previous arc at D.

Step VII. Join DA and DC.

Thus, ABCD is the required quadrilateral.

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Draw a rectangle PQRS in which PQ = 7.2 cm and QR = 5.4 cm.

Steps of construction:

I. Draw a line segment PQ = 7.2 cm.

II. At P, draw such that

III. From PX, cut off PS = 5.4 cm.

IV. At Q, draw such that .

V. From QY, cut off QR = 5.4 cm.

VI. Join R and S.

Thus, PQRS is the required rectangle.

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Draw a rhombus ABCD such that BD = 5.6 cm and AC = 6.6 cm.

Steps of construction:

I. Draw a line segment AC = 6.6 cm.

II. Draw perpendicular bisector XY of AC, which meets AC at M.

III. With centre M and radius =

i.e. 2.8 cm, draw arcs to intersect XY at B and D.

IV. Join AB, BC, CD and AD.

Thus, ABCD is the required rhombus.

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Construct a quadrilateral ABCD such that AB = 4.5 cm, BC = 3.2 cm, CD = 5 cm, DA - 2.6 cm and BD = 4.5 cm.

Steps of construction:

I. Draw a line AB = 4.5 cm.

II. With centre A and radius = 2.6 cm, draw an arc.

III. With centre B and radius = 4.5 cm, draw another arc such that it intersects the previous arc at D.

IV. With centre D and radius = 5 cm, draw an arc.

V. Again with centre B and radius = 3.2 cm, draw another arc to intersect the previous arc at C.

VI. Join AD, BC and DC.

Thus, ABCD is the required quadrilateral.

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Draw a quadrilateral in which AB = 4.5 cm, BC = 5.1 cm, CD = 3.9 cm, ∠B = 90° and ∠C = 120°.

Steps of construction:

I. Draw a line segment AB = 4.5 cm.

II. At B, construct

III. From cut off BC = 5.1 cm.

IV. AT C, draw such that

V. From cut off CD = 3.9 cm.

VI. Join AD.

Thus, ABCD is the required quadrilateral.

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