Geometry deals with properties and relations of lines, angles, surfaces, and solids. A point has no length, breadth or thickness and represents a position. A line extends indefinitely in both directions from a point. A plane has no boundaries and flat surfaces are plane surfaces. Three or more collinear points all lie on the same line.

1. GEOMETRY (LEC-02)
CONCEPT OF LINES, POINTS AND PLANES

2. 1. WHAT IS GEOMETRY?
• Ans.: Geometry is the branch of mathematics which deals with
properties and relations with the lines, angles, surfaces, and solids.
2. THREE GEOMETRICAL TERMS:
a. Lines
b. Points
c. Plane

3. 3. PLANE:
a. A solid has surface which may be flat or curved.
E.g. Triangle, rectangle, circle, etc…
b. A plane has no boundary.
c. Flat surfaces are plane surfaces.

4. 4. POINT:
a. A point is a mark of position.
b. A small dot made by pen or pencil (.) is a point.
c. A point has no length, breath or thickness.

5. LINE SEGMENT
b. Aline segment has a definite, which can be measured.
c. The line segment AB is the same thing as the line segment BA.
d. A line segment corresponds to the shortest distance two points.

6. LINE
a. A line segment extended endlessly on both sides is called a line
b. A line has no end points.
c. Two intersecting points intersect in a line.

7. 7. RAY
a. A line segment extended endlessly in one direction is
called a ray.
b. A to B is a ray denoted by AB.
c. A ray has no definite length.
.
A
B
B
Ray AB

8. 8. INTERSECTING LINES:
a. When two or more lines cross each other in a plane, they are called
intersecting lines.
b. The intersecting lines share a common point, which exists on all the
intersecting lines, and is called the point of intersection.

9. 9. PARALLEL LINES:
a. Two lines in the same plane that are at equal distance from each
other and never meet.
b. No point is common.

10. 10. CONCURRENT LINES:
a. Concurrent lines are the lines which intersect each other exactly at
one point.
b. Concurrent lines are non-parallel lines and extend indefinitely at both
the direction.

11. 11. COLLINEAR POINTS:
a. Three or more points lie in a same plane are called collinear points.
b.
The points A , B and C lie on the line m . They are collinear.

12. 12. OPEN CURVE:
An open curve is a curve in which there is no path from any of its point to the same point.

13. 13. CLOSED CURVE
This is a curve that forms a path any of its point to the same point.

14. QUESTION SERIES

15. 1. Give three examples from your environment of:
(i) Points
(ii) Portion of a line
(iii) Plane surfaces
(iv) Portion of a plane (H.1.-1)
(v) Curved surfaces (H.T.-2)

16. Ans.
a)
The three examples of points are
• Pinhole on the map
• Two walls and floor meeting at the corner
• Period at the end of the sentence

17. b)
The three examples of portion of a line are
• Thin curtain rods
• Laser beams
• Stretched power cables

18. c)
The three examples of plane surfaces are
• Surface of a white board
• Top of a table
• Surface of a wall

19. 2. Identify ray and line segment of the following:
A. B.

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

21. 4. Can you draw a line on the surface of a sphere which lies wholly on it?
Ans. No. A line cannot be drawn on the surface of the sphere which lies wholly on it.

22. 5. Write from given fig.
(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines.
(iii) lines whose point of intersection is I. (H.T.-4)
(iv) lines whose point of intersection is D. (H.T.-5)
(v) lines whose point of intersection is E. (H.T.-6)
(vi) lines whose point of intersection is A. (H.T.-7)
(vii) collinear points. (H.T.-8)

23. Ans.
(i) All pairs of parallel lines are (l, m); (m, n); ( l, n).
(ii) All pairs of intersecting lines are (l, p); (m, p); (n, p); ( l, r); (m, r); (n, r); (p, r); (l, q); (m, q); (n, q); (q,p); (q, r).
(iii) Lines whose point of intersection is I are m, p.
(iv) Lines whose point of intersection is D are l, r.
(v) Lines whose point of intersection is E are m, r.
(vi) Lines whose point of intersection is A are l, q.
(vii) Collinear points are (G, A, B, C); (D, E, J, F); (G, H, I, J, K); (A, H, D); (B, I, E); (C, F, K).

24. 6. State which of the following statements are true (T) and which are false (F):
(i) Point has a size because we can see it as a thick dot on paper.
(ii) By lines in geometry, we mean only straight lines.
(iii) Two lines in a plane always intersect in a point.
(iv) If two lines intersect at a point P, then P is called the point of concurrence of the two lines.

25. 7. Classify the following curves as open or closed:

26. THANK YOU