Mathematics NCERT Grade 6, Chapter 4: Basic Geometrical Ideas- This chapter will interact about some interesting facts that will help students to know more about the shapes around them. The chapter begins with Points followed by A Line Segment.
• A point determines a location. It is usually denoted by capital letters.
• A line segment corresponds to the shortest distance between two points
Discussion about the concept of Line, Intersecting lines, Parallel lines is also done in the chapter- Basic Geometrical Ideas
• Two distinct lines meeting at a point are called intersecting lines
• Two lines in a plane are said to be parallel if they do not meet.
After that, the chapter talks about ray, curves, and polygons.
• A ray is a portion of the line starting at a point and going in one direction endlessly.
• Any drawing done without lifting the pencil may be called a curve.
• A curve is said to be closed if its ends are joined; otherwise, it is said to be open.
• A polygon is a simple closed curve made up of line segments.
• The concept of vertex, vertices, adjacent sides, diagonals is explained.
The next topic discussed is angles, terms associated with it like vertex, arms, sides etc. Not only this, one will come across how to identify the interior and exterior of the angle
• An angle is made up of two rays starting from a common starting/initial points.
Later, triangles, quadrilaterals, and circles are explained in detail with the help of examples and required diagrams.
• A triangle is a three-sided polygon
• A quadrilateral is a four-sided polygon. Different terms associated with quadrilateral also needs to be studied like opposite sides and angles, adjacent sides and adjacent angles.
• A circle is a path of a point moving at the same distance from a fixed point.
• A region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides is called a sector.
• A region in the interior of a circle enclosed by a chord and an arc is called a segment of the circle.
• The distance around a circle is its circumference
• A diameter of a circle divides it into two equal parts; each part is a semi-circle.
Key points of the chapter Basic geometrical ideas are discussed in the end.

#### Question 1:

Use the figure to name: (a) Five points

(b) A line

(c) Four rays

(d) Five line segments

(a) The five points are D, E, O, B, and C.

(b) (c) (d) #### Question 2:

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

(a) (b) (c) (d) , #### Question 4:

How many lines can pass through (a) one given point? (b) Two given points?

(a) Infinite number of lines can pass through a single point.

(b) Only one line can pass through two given points.

#### Question 5:

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

(a) Point P lies on .

(b) and intersect at M.

(c) Line l contains E and F but not D.

(d) and meet at O.

(a) (b) (c) (d) #### Question 6:

Consider the following figure of line . Say whether following statements are true or false in context of the given figure. (a) Q, M, O, N, P are points on the line .

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

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

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

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

(f) M is point on ray .

(g) Ray is different from ray .

(h) Ray is same as ray .

(i) Ray is not opposite to ray .

(j) O is not an initial point of .

(k) N is the initial point of and .

(a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

#### Question 1:

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

(b) Closed

(c) Open

(d) Closed

(e) Closed

#### Question 2:

Draw rough diagrams to illustrate the following:

(a) Open curve (b) Closed curve.

(a) Open curve (b) Closed curve #### Question 3:

Draw any polygon and shade its interior. #### Question 4:

Consider the given figure and answer the questions:

(a) Is it a curve? (b) Is it closed? (a) Yes

(b) Yes

#### 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.

(a) (b) (c) This is not possible as the polygon having the least number of sides is a triangle, which has three sides in it.

#### Question 1:

Name the angles in the given figure. #### Question 2:

In the given diagram, name the point (s) (a) In the interior of ∠DOE

(b) In the exterior of ∠EOF

(c) On ∠EOF

(a) A

(b) C, A, D

(c) B, E, O, 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.

(a) ∠COD and ∠AOB have point O in common.

(b) ∠AOB and ∠BOC have points O and B in common.

(c) ∠AOB and ∠BOC have points O, E, B in common.

(d) ∠BOA and ∠COA have points O, E, D, A in common.

(e) Ray is common between ∠BOC and ∠AOC.

#### 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? Point A lies on the given ΔABC.

#### Question 2: (a) Identify three triangles in the figure.

(b) Write the names of seven angles.

(c) Write the names of six line segments.

(d) Which two triangles have ∠B as common?

(c) (d) ΔABD and ΔABC
​​

##### Video Solution for basic geometrical ideas (Page: 81 , Q.No.: 2)

NCERT Solution for Class 6 math - basic geometrical ideas 81 , Question 2

#### 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?  Diagonals are PR and QS. They meet at point O which is in the interior of &mnSq1PQRS.

#### 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. (a) (b) ∠KLM and ∠KNM

∠LKN and ∠LMN

(c)  (d) ∠K, ∠L and ∠M, ∠N

∠K, ∠N and ∠L, ∠M
​​

##### Video Solution for basic geometrical ideas (Page: 82 , Q.No.: 2)

NCERT Solution for Class 6 math - basic geometrical ideas 82 , Question 2

#### Question 1:

From the figure, identify: (a) The centre of circle (e) Two points in the interior

(b) Three radii (f) a point in the exterior

(c) a diameter (g) a sector

(d) a chord (h) a segment

(a) O

(b) (c) (d) (e) O, P

(f) Q

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##### Video Solution for basic geometrical ideas (Page: 84 , Q.No.: 1)

NCERT Solution for Class 6 math - basic geometrical ideas 84 , Question 1

#### Question 2:

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

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

(a) Yes. The diameter is the longest possible chord of the circle.

(b) No

#### Question 3:

Draw any circle and mark

(a) Its centre (e) a segment

(b) a radius (f) a point in its interior

(c) a diameter (g) a point in its exterior

(d) a sector (h) an arc (a) O

(b) (c) (d) COA

(e) DE

(f) O

(g) F

(h) ​​

##### Video Solution for basic geometrical ideas (Page: 84 , Q.No.: 3)

NCERT Solution for Class 6 math - basic geometrical ideas 84 , Question 3

#### 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.