Class 6 maths

Chapter Basic Geometrical Concept

Exercise 4.1 – Solutions

1. How many lines can be drawn through a given point?

Answer: Infinitely many lines can be drawn through a given point.

2. How many lines can be drawn through two distinct given points?

Answer: Only one line can be drawn through two distinct given points.

3. How many lines can be drawn through three collinear points?

Answer: Only one line can be drawn through three collinear points because all the three points lie on the same straight line.

4. Mark three non-collinear points A, B and C in your notebook. Draw lines through these points taking two at a time and name these lines. How many such different lines can be drawn?

Answer: The lines drawn are: Line AB, Line BC, Line CA

Therefore, total different lines = 3.

5. Use the adjoining figure to name:

(i) Five points

Answer: O, B, C, D, E

(ii) A line

Answer: Line BD

(iii) Four rays

Answer: Ray OB,Ray OC, Ray OD, Ray OE

(iv) Five line segments

Answer: OB,OC,OD,OE,DE

6. Use the adjoining figure to name:

(i) Line containing point E

Answer: Line AE

(ii) Line passing through A

Answer: Line AE

(iii) Line on which point O lies

Answer: Line CO

(iv) Two pairs of intersecting lines

Answer:1. Lines AE and CO

2. Lines AE and EF

7. From the adjoining figure, write:

(i) Collinear points.

Answer: Collinear points are the points lying on the same straight line.

From the figure:

A, D, C are collinear.

B, D, E are collinear.

A, E lie on the same line.

B, C lie on the same line.

Collinear points: 

•A, D, C,

•B, D, E

•A, B, p)

(ii) Concurrent lines and their points of concurrence.

Answer: Concurrent lines are the lines passing through the same point.

From the figure:

Lines p, q and m are concurrent at A.

Lines p, l and n are concurrent at B.

Concurrent lines and their point of concurrence:

•p, q, m → A

•p, l, n → B

Exercise 4.2 Solutions

Q1. How many angles are there in the adjoining figure? Name them.

Answer: There are 4 angles.

They are:

•∠DAB

•∠ABC

•∠BCD

•∠CDA

Q2. In the adjoining figure, name the points:

(i) In the interior of ∠DOE

Answer: A

(ii) In the exterior of ∠EOF

Answer: C, D

(iii) On ∠EOF

Answer: O, B, E, F