Class 6 - Maths - Basic Geometrical Ideas

Exercise 4.1

Question 1.

Use the figure to name:

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments Answer:

(a) Five points are: O, B, C, D, and E

(b) A line: DE, DB, OE, and OB

(c) Four rays: OD, OE, OC, and OB

(d) Four line segments: DE, OE, OC, OB, and OD

Question 2.

Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given. Answer:

All lines in which we choose only two letters at a time are given as:

AB, AC, AD, BC, BD, CD, BA, CA, DA, CB, DB, DC

Question 3.

Use the figure to name:

(a) Line containing point E.

(b) Line passing through A.

(c) Line on which O lies.

(d) Two pairs of intersecting lines Answer:

(a) A line containing E = AE or FE

(b) A line passing through A = AE or DE

(c) A line on which O lies = CO or OC

(d) Two pairs of intersecting lines are: AD, CO and AE, FE

Question 4.

How many lines can pass though:

(a) one given point? (b) two given points

Answer:

(a) Let there is a point O. Now from the figure, we can see that

Infinite number of lines can pass through one given point. (b) If there is only two points given, then only one line can pass through two given points as shown in the figure: Question 5:

Draw a rough figure and label suitably in each of the following cases:

(a) Point P lies on AB   (b) XY and PQ intersect at M.

(c) Line contains E and F but not D. (d) OP and OQ meet at O.

Answer:

(a) Point P lies on AB (b) XY and PQ intersect at M (c) Line contains E and F but not D (d) OP and OQ meet at O Question6.

Consider the following figure of line MN. Say whether following statements are true or false in the context of the given figure:

(a) Q, M, O, N, P are points on the line MN.

(b) M, O, N are points on a line segment MN.

(c) M and N are end points of line segment MN.

(d) O and N are end points of line segment OP.

(e) M is one of the end points of line segment QO.

(f) M is point on ray OP.

(g) Ray OP is different from ray QP.

(h) Ray OP same as ray OM.

(i) Ray OM is not opposite to ray OP.

(j) O is not an initial point of OP.

(k)O is not an initial point of NM and NP. Answer:

(a) True

In the given figure, Q, M, O, N, P are points on the line MN.

(b) True

In the given figure, M, O, N are points on the line MN.

(c) True

In the given figure, M and N are end points of line segment MN.

(d) False

In the given figure, O and N are not end points of line segment OP.

(e) False

In the given figure, M is not the end points of line segment QO. It is the middle point of it.

(f) False

In the given figure, M is not the point on ray OP. O is the point on ray OP

(g) True

In the given figure, ray OP and ray OQ both have different directions.

(h) False

In the given figure, ray OP and ray OM both have different directions.

(i) False

In the given figure, ray OP and ray OM both have different directions.

(j) False

In the given figure, O is an initial point of OP.

(k) True

In the given figure, O is not an initial point of NM and NP.

Exercise 4.2

Question 1.

Classify the following curves as (i) Open or (ii) Closed. Answer:

(a) It is an open curve since there is not boundary inside it.

(b) It is a closed curve because we cannot enter inside without crossing the boundary line.

(c) It is an open curve because we can enter inside without crossing the boundary line.

(d) It is a closed curve because we cannot enter inside without crossing the boundary line.

(e) It is a closed curve because we cannot enter inside without crossing the boundary line.

Question 2.

Draw rough diagrams to illustrate the following:

(a) Open curve

(b) Closed curve

Answer:

(a) A curve is called an open curve if it has no boundary and we can reach inside without

crossing the boundary of it. (b) ) A curve is called a closed curve if it has boundary and we cannot reach inside without

crossing the boundary of it. Question 3.

Draw any polygon and shade its interior.

Answer:

A figure is a polygon if it is a simple closed figure made up entirely of line segments.

Let ABCDE is a polygon. Question 4.

Consider the given figure and answer the questions:

(a) Is it a curve?

(b) Is it closed? Answer:

(a) Yes, it is a curve.

(b) Yes, it is closed.

Question 5.

Illustrate, if possible, each one of the following with a rough diagram:

(a) A closed curve that is not a polygon.

(b) An open curve made up entirely of line segments.

(c) A polygon with two sides.

Answer:

(a) Yes, we can draw a closed curve that is not a polygon. (b) Yes, we can draw an open curve made up entirely of line segments (c) Polygon with two sides cannot be draw.

Exercise 4.3

Question 1.

Name the angles in the given figure: Answer:

There are four angles in given figure: ÐABC, ÐCDA, ÐDAB and ÐDCB

Question 2.

In the given diagram, name the point(s):

(a) In the interior of ÐDOE.   (b) In the exterior of ÐEOF.   (c) On ÐEOF. Answer:

(a) Point interior of ÐDOE: A

(b) Points exterior of ÐEOF: C, A, D

(c) Points on ÐEOF: E, O, B, F

Question 3.

Draw rough diagrams of two angles such that they have:

(a) One point in common.       (b) Two points in common. (c) Three points in common.

(d) Four points in common.    (e) One ray in common.

Answer:

(a) One point in common: Here, ÐCOD and ÐAOB have point O in common.

(b) Two points in common: Here, ÐBOC and ÐAOB have points O and B in common.

(c) Three points in common: Here, ÐBOC and ÐAOB have points O, E and B in common.

(d) Four points in common: Here, ÐBOA and ÐCOA have points O, E, D and A in common.

(e) One ray in common: Here, Ray OC is common between ÐBOC and ÐAOC.

Exercise 4.4

Question 1.

Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?

Answer: From the figure, we can see that A is neither interior of the figure nor exterior of triangle. It is

a vertex of the triangle ABC.

Question 2.

(a) Identify three triangles in the figure:   (b) Write the names of seven angles.

(c) Write the names of sic line segments.   (d) Which two triangles have ÐB as common? Answer:

(a) The three triangles are: DADC, DABD, and DABC

(b) Angles are: Ð ADB, Ð ADC, Ð ABD, Ð ACD, Ð BAD, Ð CAD, and Ð BAC

(c) Line segments are: AB, AC, AD, BD, DC, and BC

(d) Triangles having common ÐB: DABD and DABC

Exercise 4.5

Question 1.

Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?

Answer: Here, PQRS is a quadrilateral. Diagonal PR and diagonal SQ meet at O, which is inside the

Quadrilateral PQRS.

Question 2.

Draw a rough sketch of a quadrilateral KLMN. State:

(a) Two pairs of opposite sides.   (b) Two pairs of opposite angles.

(c) Two pairs of adjacent sides.   (d) Two pairs of adjacent angles.

Answer: (a) Pair of opposite sides: KL and MN, KN and LM

(b) Pair of opposite angles: Ð K and Ð M, Ð L and Ð N

(c) Pair of adjacent sides: KN and NM, KL and LM

(d) Pair of adjacent angles: Ð K and Ð N, Ð L and Ð M

Question 3.

Investigate:

Use strip and fasteners to make a triangle and a quadrilateral. Try to push inward at any one

vertex of the triangle. Do the same to the quadrilateral. Is the triangle distorted? Is  the

quadrilateral distorted? Is the triangle rigid? Why is it that structures like electric towers

make use of triangular shapes and not quadrilateral?

Answer:

O is common to both the angles Ð AOC and Ð BOC.

No, the triangle is not distorted but the quadrilateral is distorted and also the triangle is rigid.

Structures like electric towers make use of triangular shape so that they could not be distorted

and they could be rigid.

Exercise 4.6

Question 1.

From the figure, identify:

(a) The centre of circle.   (b) Three radii.    (c) A diameter.    (d) A chord.    (e) Two points in the

interior. (f) A point in the exterior.   (g) A sector.   (h) A segment Answer:

From the figure:

(a) O is the centre.

1. b) Three radii: OA, OB and OC

(c) A diameter: AC

(d) A chord: ED

(e) Interior points: O, P

(f) Exterior point: Q

(g) A sector: OAB

(h) A segment: ED

Question 2.

(a) Is every diameter of a circle also a chord?

(b) Is every chord of a circle also a diameter?

Answer:

(a) Yes, every diameter of a circle is also a chord.

(b) No, every chord of a circle is not a diameter.

Question 3.

Draw any circle and mark:

(a) Its centre.   (b) A radius.   (c) A diameter.   (d) A sector.

Answer:

In the given figure, O is the center of circle, OB, AO are the radii of the circle,

AC is the diameter and AOB is the sector of the circle. Question 4.

Say true or false:

(a) Two diameters of a circle will necessarily intersect.

(b) The centre of a circle is always in its interior.

Answer:

(a) True.

Two diameters of a circle will necessarily intersect.

(b) True.

The centre of a circle is always in its interior.

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