- A point determines a location. It is usually denoted by capital letters.
- A line segment corresponds to the shortest distance between two points.
- 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.
- 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.
- An angle is made up of two rays starting from a common starting/initial points.
- 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.
Page No 74:
Question 1:
Use the figure to name:
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Answer:
(a) The five points are D, E, O, B, and C.
(b)
(c)
(d)
Page No 74:
Question 2:
Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.
Answer:
Page No 75:
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)
(b)
(c)
(d) ,
Page No 75:
Question 4:
How many lines can pass through (a) one given point? (b) Two given points?
Answer:
(a) Infinite number of lines can pass through a single point.
(b) Only one line can pass through two given points.
Page No 75:
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.
Answer:
(a)
(b)
(c)
(d)
Page No 75:
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.
Answer:
(a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(i) False
(j) False
(k) True
Page No 78:
Question 1:
Classify the following curves as (i) Open or (ii) Closed.
Answer:
(a) Open
(b) Closed
(c) Open
(d) Closed
(e) Closed
Page No 78:
Question 2:
Draw rough diagrams to illustrate the following:
(a) Open curve (b) Closed curve.
Answer:
(a) Open curve
(b) Closed curve
Page No 78:
Question 3:
Draw any polygon and shade its interior.
Answer:
Page No 78:
Question 4:
Consider the given figure and answer the questions:
(a) Is it a curve? (b) Is it closed?
Answer:
(a) Yes
(b) Yes
Page No 78:
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)
(b)
(c) This is not possible as the polygon having the least number of sides is a triangle, which has three sides in it.
Page No 80:
Question 1:
Name the angles in the given figure.
Answer:
∠BAD, ∠ADC, ∠DCB, ∠CBA
Page No 80:
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
Answer:
(a) A
(b) C, A, D
(c) B, E, O, F
Page No 80:
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)
∠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.
Page No 81:
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:
Point A lies on the given ΔABC.
Page No 81:
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?
Answer:
(a) ΔABC, ΔACD, ΔADB
(b) ∠ABC, ∠ADB, ∠ADC, ∠ACB, ∠BAD, ∠CAD, ∠BAC
(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
Page No 82:
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:
Diagonals are PR and QS. They meet at point O which is in the interior of &mnSq1PQRS.
Page No 82:
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)
(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
Page No 84:
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
Answer:
(a) O
(b)
(c)
(d)
(e) O, P
(f) Q
(g) AOB (shaded region)
(h) DE (shaded region)
Video Solution for basic geometrical ideas (Page: 84 , Q.No.: 1)
NCERT Solution for Class 6 math - basic geometrical ideas 84 , Question 1
Page No 84:
Question 2:
(a) Is every diameter of a circle also a chord?
(b) Is every chord of circle also a diameter?
Answer:
(a) Yes. The diameter is the longest possible chord of the circle.
(b) No
Page No 84:
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
Answer:
(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
Page No 84:
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. They will always intersect each other at the centre of the circle.
(b) True
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