NCERT solutions for Mathematics [English] Class 6 chapter 14 - Practical Geometry [Latest edition]

Draw a circle of radius 3.2 cm.

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

1. A is on the circle.

2. B is in the interior of the circle.

3. 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 `overline("AB")` and `overline"CD"` 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.

Given `overline"AB"` of length 3.9 cm, construct `overline"PQ"`  such that the length of `overline"PQ"` is twice that of `overline"AB"`. Verify by measurement.

(Hint: construct `overline"PX"` such that length of `overline"PX"` = length of  `overline"AB"`; then cut off  `overline"XQ"` such that `overline"XQ"` also has the length of `overline"AB"`.) 

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

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

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

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

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

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

Now draw a perpendicular `overline"XY"` to at Y. (use ruler and compasses) 

Draw `overline"AB"` 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 `overline"XY"` whose length is 10.3 cm.

1. Take any point P on the bisector drawn. Examine whether PX = PY

2. If M is the midpoint of `overline"XY"`, 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 `overline"PQ"` of length 6.1 cm as diameter, draw a circle.

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

Repeat Question 6, if `overline"AB"` 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 `overline"OA"` and `overline"OB"`. Let them meet at P. Is PA = PB ?

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 compass, angle of 60° measure.

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.