Solution of Chapter 14. Practical Geometry (NCERT - Mathematics Book)

Draw a circle of radius 3.2 cm.

With the same centre O, draw two circles of radii 4 cm and 2.5 cm.

Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtaines?

What figure is obtained, if the diameters are perpendicular to each other? How do you check your answer?

Draw any circle and mark points A, B and C such that

(a) A is on the circle.

(b) B is in the interior of the circle.

(c) C is in the exterior of the circle.

Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D.

Examine whether and are at right angles.

Draw a line segment of length 7.3 cm, using a ruler.

Construct a line segment of length 5.6 cm, using ruler and compasses.

Construct of length 7.8 cm. From this, cut off of length 4.7 cm. Measure .

Given of length 3.9 cm, construct such that the length of is twice that of . Verify by measurement.

Given of length 7.3 cm and of length 3.4 cm, construct a line segment such that the length of is equal to the difference between the lengths and . Verify by measurement.

Draw any line segment PQ. Without measuring , construct a copy of .

Given some line segment AB, whose length you do not know, construct such that the length of is twice that of .

Draw any line segment AB. Mark any point M on it. Through M, draw a perpendicular to . (Use ruler and compasses)

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Draw any line segment PQ. Take any point R not lying on it. Through R, draw a perpendicular to . (use ruler and set square)

Draw a line l and a point X on it. Through X, draw a line segment XY perpendicular to l.

Now draw a perpendicular to at Y. (use ruler and compasses)

Draw of length 7.3 cm and find its axis of symmetry.

Draw a line segment of length 9.5 cm and construct its perpendicular bisector.

Draw the perpendicular bisector of whose length is 10.3 cm.

(a) Take any point P on the bisector drawn. Examine whether PX = PY.

(b) If M is the mid-point of , what can you say about the lengths MX and XY?

Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.

With of length 6.1 cm as diameter, draw a circle.

Draw a circle with centre C and radius 3.4 cm. Draw any chord . Construct the perpendicular bisector of and examine if it passes through C.

Repeat question 6, if happens to be a diameter.

Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of and . Let them meet at P. Is PA = PB.

Draw ∠POQ of measure 75° and find its line of symmetry.

Draw an angle of measure 147° and construct its bisector.

Draw a right angle and construct its bisector.

Draw an angle of measure 153° and divide it into four equal parts.

Construct with ruler and compasses, angles of following measures:

(a) 60° (b) 30°

(c) 90° (d) 120°

(e) 45° (f) 135°

Draw an angle of measure 45° and bisect it.

Draw an angle of measure 135° and bisect it.

Draw an angle of 70°. Make a copy of it using only a straight edge and compasses.

Draw an angle of 40°. Copy its supplementary angle.