UNIT 3
Text One
|
A point. A straight line.
A plane.
The intersection of a straight line and a plane is a point.
The intersection of two planes is a straight line.
Two points determine a straight line. For example, points A and B determine line a. A straight line is determined by two points. For example, line a is determined by points A and B. Points which lie in the same straight line are called collinear. For example, points A and B are collinear. Points which do not lie in the same straight line are known as noncollinear. For example, points A,B, and C are noncollinear. |
|
Three noncollinear determine a plane. A plane is determined by three noncollinear points. Or: A plane is determined by a line and a point outside the line. |
Exercise: True or false?
1. A line is determined by one point.
2. Three points which lie in the same line are collinear.
3. Noncollinear points lie in the same straight line.
4. The number of points which determine a plane is greater than two.
Text Two
|
A circle and a point. The point is on the circle.
A circle and a point. The point is outside the circle.
A circle and a point. The point is within the circle. It is called the centre. All points on the circle are equidistant from the centre, i.e. they are at the same distance from the centre.
For example, if C is the centre of the circle and if A and B are points on the circle, then CA=CB, i.e. A and B are at the same distance from C. |
|
A circle is a set of all points in a plane which are equidistant from a point called the centre. A circle divides a plane into three sets of points: 1. The set of all points within the circle. 2. The set of all points outside the circle. 3. The set of all points on the circle. |
Exercise: True or false?
1. A circle may have two centres.
2. A circle is a set of straight lines.
3. A circle is a set of points.
4. A circle divides a plane into three sets of triangles.