Practical Geometry

Question

Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

Solution

The steps of construction are as follows.

(i) Draw a line l and take a point P on line l. Then, draw a perpendicular at point P.

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(ii) Adjusting the compasses up to the length of 4 cm, draw an arc to intersect this perpendicular at point X. Choose any point Y on line l. Join X to Y.

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(iii) Taking Y as centre and with a convenient radius, draw an arc intersecting l at A and XY at B.

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(iv) Taking X as centre and with the same radius as before, draw an arc CD cutting XY at E.

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(v)Adjust the compasses up to the length of AB. Without changing the opening of compasses and taking E as the centre, draw an arc to intersect the previously drawn arc CD at point F.

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(vi) Join the points X and F to draw a line m.

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Line m is the required line which is parallel to line l.

Some More Questions From Practical Geometry Chapter

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Practical Geometry

Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

Some More Questions From Practical Geometry Chapter

Draw ΔPQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of
triangle is this?

Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.

Construct ΔDEF such that DE = 5 cm, DF = 3 cm and m∠EDF = 90°.

Construct an isosceles triangle in which the lengths of each of its equal sides
is 6.5 cm and the angle between them is 110°.

Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m∠C = 60°.

Construct ΔABC, given m∠A = 60°, m∠B = 30° and AB = 5.8 cm.

Construct ΔPQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°.
(Hint: Recall angle sum property of a triangle).

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E =
110° and m∠F = 80°. Justify your answer.

Construct the right angled ΔPQR, where m∠Q = 90°, QR = 8 cm and PR = 10 cm

Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

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For Daily Free Study Material Join wiredfaculty

Practical Geometry

Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

Some More Questions From Practical Geometry Chapter

Draw ΔPQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type oftriangle is this?

Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.

Construct ΔDEF such that DE = 5 cm, DF = 3 cm and m∠EDF = 90°.

Construct an isosceles triangle in which the lengths of each of its equal sidesis 6.5 cm and the angle between them is 110°.

Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m∠C = 60°.

Construct ΔABC, given m∠A = 60°, m∠B = 30° and AB = 5.8 cm.

Construct ΔPQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°.(Hint: Recall angle sum property of a triangle).

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E =110° and m∠F = 80°. Justify your answer.

Construct the right angled ΔPQR, where m∠Q = 90°, QR = 8 cm and PR = 10 cm

Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Draw ΔPQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of
triangle is this?

Construct an isosceles triangle in which the lengths of each of its equal sides
is 6.5 cm and the angle between them is 110°.

Construct ΔPQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°.
(Hint: Recall angle sum property of a triangle).

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E =
110° and m∠F = 80°. Justify your answer.