R d sharma mathematics solutions class 6 Solutions for Chapter 18 geometrical constructions

Exercises in Chapter 18 geometrical constructions Grade 6

Geometrical Constructions Exercise 19.1

Geometrical Constructions Exercise 19.2

Geometrical Constructions Exercise 19.3

Geometrical Constructions Exercise 19.4

Geometrical Constructions Exercise 19.5

Geometrical Constructions Exercise 19.6

Questions in Geometrical Constructions Exercise 19.1

Construct line segments whose lengths are:

(i) 4.8 cm

(ii) 12 cm 5 mm

(iii) 7.6 cm

Construct two segments of length 4.3 cm and 3.2 cm. Construct a segment whose length is equal to the sum of the lengths of these segments.

Questions in Geometrical Constructions Exercise 19.2

How many lines can be drawn which are perpendicular to a given line and pass through a givenpoint lying

(i) outside it?

(ii) on it?

Draw a line PQ. Take a point R on it. Draw a line perpendicular to PQ and passing throughR.

(Using (i) ruler and a set-square (ii) ruler and compasses)

Draw a line l. Take a point A, not lying on l. Draw a line m such that m ⊥ l and passing throughA.

(Using (i) ruler and a set-square (ii) ruler and compasses)

Draw a line AB and take two points C and E on opposite sides of AB. Through C, draw CD ⊥ AB and through E draw EF ⊥ AB.

(Using (i) ruler and a set-square (ii) ruler and compasses)

Draw a line segment AB of length 10 cm. Mark a point P on AB such that AP = 4 cm. Draw a line through P perpendicular to AB.

Draw a line segment PQ of length 12 cm. Mark a point O outside this segment. Draw a line throughO perpendicular to PQ.

Using a protractor, draw ∠BAC measures 70° On side AC, take a point P, such that AP = 2 cm. From P draw a line perpendicular to AB.

Draw a line segment AB of length 8 cm. At each end of this line segment, draw a line perpendicular to AB. Are these two lines parallel?

Using a protractor, draw ∠BAC of measure 45° Take a point P in the interior of ∠BAC. From P drawn line segments PM and PN such that PM ⊥ AB and PN ⊥ AC, Measure ∠MPN.

Draw an angle and label it as ∠BAC. Draw its bisector ray AX and take a point P on it. From P draw line segments PM and PN, such that PM ⊥ AB and PN ⊥ AC, where M and N are respectively points on rays AB and AC. Measure PM and PN. Are the two lengths equal?

Questions in Geometrical Constructions Exercise 19.3

Draw a line segment of length 8.6 cm. Bisect it and measure the length of eachpart.

Draw a line segment AB of length 5.8 cm. Draw the perpendicular bisector of this line segment.

Draw a circle with centre at point O and radius 5 cm. Draw its chord AB, draw theperpendicular bisector of line segment AB. Does it pass through the centre of the circle?

Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect?

Draw a line segment of length 10 cm and bisect it. Further bisect one of the equal parts and measureits length.

Draw a line segment AB and bisect it. Bisect one of the equal parts to obtain a line segment of length 1/2 (AB).

Draw a line segment AB and by ruler and compasses, obtain a line segment of length 3/4 (AB).

Questions in Geometrical Constructions Exercise 19.4

Construct the following angles with the help of a protractor: 45° , 67° , 38° , 110° , 179° , 98° , 84°

Draw two rays PQ and RS as shown in Fig. 19.14 (i) and (ii). Using protractor, construct angles of 15° and 138° with one arm PQ and RS respectively.

Questions in Geometrical Constructions Exercise 19.5

Draw an angle and label it as ∠BAC. Construct another angle, equal to∠BAC.

Draw an obtuse angle. Bisect it. Measure each of the angles so obtained.

Using your protractor, draw an angle of measure 108° . With this angle as given, drawn an angle of 54° .

Using protractor, draw a right angle. Bisect it to get an angle of measure 45° .

Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.

Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

Using ruler and compasses only, draw a right angle.

Using ruler and compasses only, draw an angle measure of 135°.

Using a protractor, draw an angle of measure 72° . With this angle as given, draw angles of measure 36° and 54° .

Questions in Geometrical Constructions Exercise 19.6

Construct an angle of 60° with the help of compasses and bisect it by paper folding.

Construct the following angles with the help of ruler and compasses only:

(i) 30°

(ii) 90°

(iii) 45°

(iv) 135°

(v) 150°

(vi) 105°

Construct a rectangle whose adjacent sides are 8 cm and 3 cm.

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Chapters in this book

Knowing your numbers

Playing with numbers

Whole Numbers

Operations on whole numbers

Negative number and integers

Fractions

Decimals

Introduction to Algebra

Ratio, Proportion and Unitary Method

Basic Geometrical Concepts

Angles

Triangles

Circles

Pair of Lines and Transversal

Understanding Three Dimensional Shapes

Symmetry

Basic Geometrical Tools

Geometrical Constructions

Mensuration

Data Handling Presentation Of Data

Data Handling – II

Data Handling Bar Graphs