# Solution of Chapter 4 Basic Geometrical Ideas Class 6th Mathematics (2023-24)

- Posted by doubtout
- Categories Class 6th Math
- Date June 30, 2020
- Comments 0 comment

** Exercise 4.1 **

**1. Use the figure to name:**

**(a) Five points**

**(b) A-line**

**(c) Four rays**

**(d) Five line segments**

**Solutions:**

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

(b) A line is

(c) Four rays are , , and .

(d) Five line segments are , , , and

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

**Solutions:**

The lines are , , , , , , , , , , ,

**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.**

**Solutions:**

(a) Line containing point E is

(b) Line passing through A is

(c) Line on which O lies is

(d) Two pairs of intersecting lines are , and ,

**4. How many lines can pass through (a) one given point? (b) two given points?**

**Solutions:**

**(a) **Countless lines can pass through a given point.

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

**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.**

**Solutions:**

**(a)**

(b)

**(c)**

(d)

**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 .**

**Solutions:**

(a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

========================================================================================================

** Exercise 4.2 **

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

**Solutions:**

**(a) **The given curve is an open curve

(b) The given curve is a closed curve

(c) The given curve is an open curve

(d) The given curve is a closed curve

(e) The given curve is a closed curve

**2. Draw rough diagrams to illustrate the following:**

**(a) Open curve**

**(b) Closed curve**

**Solutions**

**(a) **The below figure is an open curve

**(b) **The below figure is a closed curve

**3. Draw any polygon and shade its interior.**

**Solutions:**

The below figure is a polygon with a shaded interior.

**4. Consider the given figure and answer the questions:**

**(a) Is it a curve?**

**(b) Is it closed?**

**Solutions:**

**(a) **Yes, it is a curve

(b) Yes, it is a closed curve

**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.**

**Solutions:**

**(a) **The below figure is a closed figure but not a polygon.

**(b) **The below figure is an open curve made up entirely of line segments.

(c) No, it’s not possible, as the polygon with the least number of sides is a triangle, which has three sides.

========================================================================================================

** Exercise 4.3 **

**1. Name the angles in the given figure.**

**Solutions:**

The angles are ∠DAB, ∠ABC, ∠BCD and ∠CDA

**2. In the given diagram, name the points(s)**

**(a) In the interior of ∠DOE**

**(b) In the exterior of ∠EOF**

**(c) On ∠EOF**

**Solutions:**

**(a) **The point in the interior of ∠DOE is A

(b) The points in the exterior of ∠EOF is C, A and D

(c) The points on ∠EOF are E, B, O and F

**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**

**Solutions:**

**(a) **O is the common point between ∠COD and ∠AOB

(b) O and B are common points between ∠AOB and ∠BOC

(c) O, E and B are common points between ∠AOB and ∠BOC

(d) O, E, D and A are common points between ∠BOA and ∠COA

(e) OC is a common ray between ∠BOC and ∠AOC