The document RD Sharma Solutions -Ex-10.1, Basic Geometrical Concepts, Class 6, Maths Class 6 Notes | EduRev is a part of the Class 6 Course RD Sharma Solutions for Class 6 Mathematics.

All you need of Class 6 at this link: Class 6

**Question 1. Make three points in your notebook and name them.**

**Solution : **Three points, namely A,P and H can be marked as follows

**Question 2. Draw a line in your notebook and name it using a small letter of the alphabet**

**Solution : **Let us draw a line and name it l

**Question 3. Draw a line in your notebook and name it by using two points on it**

**Solution : **Let us first draw a line. Two points on it are P and Q. now, the line can be written as line PQ

**Question 4. Give three examples from your environment of:**

**i) Pointsii) Portion of a lineiii) Plane of the surfaceiv)Portion of the linev) Curved surface**

**i)** The period at the end of the sentence, a pinhole on the map and the point at which two walls and the floor meet at the corner of the room.

**ii) **Tightly stretched power cables, laser beams, and thin curtain rods

**iii) **The surface of a smooth wall, the surface of the top of a table and the surface of a smooth white board**iv) **The surface of the sheet of the paper, the surface of calm water in a swimming pool and the surface of a mirror

**v) **The surface of a gas cylinder, the surface of a tea pot and the surface of an ink pot .

**Question 5. ****There are a number of ways by which we can visualize a portion of a line. State whether the following represent a portion of line or not:**

**i) A piece of elastic stretched to the breaking point**

**ii) Wire between two electric poles**

**iii) The line thread by which a spider lowers itself****Answer:****i) **Yes**ii)** No**iii)** Yes**Question 6. Can you draw a line on the surface of a sphere which lies wholly on it?**

**Solution : **No, we cannot draw a line on the surface of the sphere, which lies wholly on it.

**Questions 7. Make appoint on the sheet of a paper and draw a line passing through it. How many lines can you draw through this point?**

**Solution : **Unlimited number of lines can be drawn passing through a point L

**Question 8. Mark any two points P and Q in your notebook and draw a line passing through the points.**

**How many lines can you draw passing through this both points?**

**Solution : **We have two points P and Q and we draw a line passing through these two points.

Only one line can be drawn passing through these two points.

**Question 9. Give an example of the horizontal plane and a vertical plane from your environment.**

**Solution : **Ceiling of a room is an example of a horizontal plane in our environment.

Wall of a room is an example of a vertical plane in our environment.

**Question 10. How many lines may pass through one given point , two given point , any three collinear points?**

**Solution : **Lines passing through one point â€“ **unlimited**

Lines passing through two points â€“** one**

Lines passing through any three collinear points â€“** one**

**Question 11. Is it ever possible for exactly one line to pass through three points?**

**Solution : **Yes, it is possible if three points lie on a straight line

**Question 12. Explain why is not possible for a line to have a mid point?**

**Solution : **The length of the line is infinite. Thus, it is not possible to find its midpoint. On the other hand, we can find, we can find the midpoint of a line segment

**Question 13. Mark three non â€“ collinear points points A,B,C in your notebook . Draw the lines through the points taking two at a time. Name these lines. How many such different lines can be drawn ?**

**Solution : **These are three non â€“ collinear points A,B,C

Three lines can be drawn through these points. These three lines are AB, BC and AC

**Question 14. ****Coplanar points points are the points that are in the same plane. Thus,**

**i) Can 150 points be coplanar?****Answer: **Yes,

A group of points that lie in the same plane are called co planar points.

Thus, it is possible that 150 points can be co-planar.

**ii) Can 3 points be non â€“ co planar?**

**Answer:** No

3 points will be coplanar because we can have a plane that can contain 3 points on it.

Thus, it is not possible that 3 points will be non â€“ coplanar.

**Question 15. Using a ruler, check whether the following points given in the figure are collinear or not?**

**Answer:**

**i)** D,A and C are **collinear points**

**ii)**A,B and C are non â€“ **collinear points**

**iii)** A,B and E are **collinear points**

**iv)** B,C and E are non â€“ **collinear points**

**Question 16. Lines p, q is coplanar. So are the lines p, r. Can we conclude that the lines p, q, r are coplanar?**

**Solution : **No, p,q and r are not necessarily coplanar.

**Example â€“ **if we take p as intersecting line of two consecutive walls of a room , q as a line on the first wall and r on the second wall whose (both walls) intersection is line p

Thus we can see that p,q and r are not coplanar.

**Question 17. ****Give three examples of each:**

**i) Intersecting lines :****Answer:**

**i) Parallel lines from your environment:****Answer:**

**Question 18. ****From the figure write:**

**Answer:**

**i)** **All pairs of intersecting lines ****Answer:** (l,m) ,(m,n) , and (l,n)

**ii)** **All pairs of intersecting lines****Answer:** (l,p) , (m,p) , ( n,p) , (l,r) , (m,r) , (n,r) ,(I,q),(m,q),(n,q) , (q,p) ,(q,r)

**iii)** Lines whose point of intersection is l**Answer:** (m,p)

**iv)** **Lines whose point of intersection is D****Answer: **(l,r)

**v)** **Lines whose point of intersection E****Answer:** (m,r)

**vi)** **Lines whose point of intersection is A****Answer:** ( l,q)

**vii)** Collinear points**Answer:** (G,A,B and C) ,(D,E,J and F) , ( G,H,I and J,K) ,(A,H,and D) ,(B,I and E) and ( C,F and K)

**Question 19. Write concurrent lines and their and their point of concurrence:**

**Answer:**

**From the given figure, we have :**

Concurrent lines can be defined as three or more lines which share the same meeting point. Clearly lines, n,q, and l are concurrent with A as the point of concurrence .

Lines, m,q and p are concurrent with B as the point of concurrence.

**Question 20. Mark four points A,B,C,D in your notebook such that no three of them are collinear . Draw all the lines which join them in pairs as shown**

**i) How many such lines can be drawn**

**Answer: **Six lines can be drawn through these four points as given in the figure.

**ii) Write the names of these lines****Answer:** These lines are AB, BC, CD, BD and AD

**iii) Name the lines which are concurrent to A**

**Answer:** Lines which are concurrent at A are AC, AB and AD

**Question 21. What is the maximum number of points of intersection of three lines in a plane? What is the minimum number?**

**Solution : **Maximum number of points of intersection of three lines in a plane will be three

Minimum number of points of intersection of three lines in a plane will be zero

**Question 22. With the help of a figure, find the maximum and minimum number of points of intersection of four lines in a plane.**

**Solution : **Maximum number of points of intersection of four lines in a plane will be six

Minimum number of points of intersection of four lines in a plane will be zero.

**Question 23. Lines p,q and r are concurrent. Also, the lines p, r and s are concurrent. Draw a figure and state whether lines p,q, r and s are concurrent or not?**

**Solution : **

Thus, lines p,q and r intersect at a common point O

Also, lines p,r, and s are concurrent

Therefore, lines p, r, and s intersect at a common point. But q and r intersect each other at O.

So, p,q and r intersect at O

Hence, p,q,r and s are concurrent . Lines p, q,r and s intersect at O

**Question 24. Lines p, q, and r are concurrent. Also lines p,s and t are concurrent . Is it always true that the lines q,r and s will be concurrent? Is it always true for lines q, r, and t?**

**Solution : **Lines p, q, and r are concurrent. So, lines p, q and r intersect at a common point O

Given lines p, s, and t are concurrent. So, lines p, s and t also intersect at a common point. However, it is not always true that q, r and s or q, r and t are concurrent.

**Question 25. Fill in the blanks in the following statements using suitable words:**

**i) A page of a book is a physical example of a****Answer: plane**

**ii) ****An inkpot has both ____________ surfaces****Answer:** curved and plane

iii) **Two lines in a plane are either______or are_______**

**Answer:** parallel or are intersecting

**Question 26. State which of the following statements are true and which are false:**

**i) **Point has a size because we can see it as a thick dot on paper â€“ **False**

**ii)** By lines in geometry , we mean only straight lines â€“ **True**

**iii)** Two lines in a plane always intersect at a point â€“ **False**

**iv) **Any plane through a vertical line is vertical â€“ **True**

**v) **Any plane through a horizontal line is horizontal â€“ **False**

**vi)** There cannot be a horizontal line in a vertical plane â€“ **False**

**vii)** All lines in a horizontal plane are horizontal â€“ **True**

**viii)** Two lines in a plane always intersect at a plane â€“ **False**

**ix)** If two lines intersect at a point P , then P is called the point of concurrence of the two lines â€“ **False**

**x)** If two lines intersect at a point P , then P is called the point of intersection of the two lines- **True**

**xi)** If A,B,C and D are collinear points D,P and Q are collinear , then points A,B,C,D,P and Q are always collinear â€“ **False**

**xii)** Two different lines can be drawn passing through two given points â€“ **False**

**xiii)** Through a given point only one line can be drawn â€“ **False**

**xiv)** Four points are collinear if any three of them lie on them lie on the same line â€“ **False**

**xv)**The maximum number of points of intersection of three lines is three â€“ **True**

**xvi)**The minimum number of points of intersection of three lines is one â€“** False**

**Question 27. Give the correct matching of the statements of column A and column B**

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!