1.1 Points, Lines And Planes

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Figure 1.2

Figure 1.2 shows two lines l and m . Line l is such that it passes through A, B and C. Hence points A B and C are collinear. In the case of points P, Q and R there can be no single line containing all three of them hence they are called non-linear.

Similarly points and lines which lie in the same plane are called coplanar otherwise they are called non-coplanar.

Axiom : A plane containing a line and a point outside it or by using the definition of a line, a plane can be said to contain three non-collinear points. Conversely, through any three non collinear points there can be one and only one plane (figure 1.3).

Axiom : If two lines intersect, exactly one plane passes through both of them (figure1.4).

Axiom : If two planes intersect their intersection is exactly one line (figure 1.5).

Figure 1.3

Lines A, B and C are contained in the same plane P or A, B and C are three non-collinear points through which one plain P can pass.

1.4

Plane Q contains intersecting lines l and m .

Figure 1.5

Planes P and Q intersect and their intersection is line l .

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Index

Introduction 1.1 Points, Lines and Planes 1.2 Line Segment 1.3 Rays and Angles 1.4 Some Special Angles 1.5 Angles made by a Transversal 1.6 Transversal Across Two Parallel Lines 1.7 Conditions for Parallelism Chapter 2

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