Introduction to Geometry. Definitions of point, line and plane.

1. INTRODUCTION
TO GEOMETRY

2. DEFINITIONS
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3. POINT
A POINT has no dimension.
It is represented by a dot.
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A

4. LINE
A LINE extends in one dimension. It is represented by a
straight line with two arrowheads, indicating that it extends
indefinitely in two directions.
A
B
It is denoted by:
𝐴𝐵 or 𝑙.
Collinear points are points that lie on the same line.
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5. PLANE
A PLANE extends in two dimensions. It is represented by a
shape that looks like a table or wall. It is important to note
that a plane extends indefinitely.
Coplanar points are points that lie on the same plane.
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6. NAMING COLLINEAR AND COPLANAR POINTS
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7. LINE SEGMENT
Consider the line AB, symbolized by 𝑨𝑩.
A B
The line segment or segment, 𝐴𝐵 symbolized by 𝑨𝑩 consists of
the end points A and B, and all points on 𝐴𝐵 that are between A
and B.
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8. RAY
The ray AB, symbolized by 𝑨𝑩 consists of the initial point A, and
all points on 𝐴𝐵 that lie on the same side of A as point B.
Note: 𝑨𝑩 is the same as 𝑩𝑨.
𝑨𝑩 is the same as 𝑩𝑨.
However, 𝑨𝑩 and 𝑩𝑨 are not the same.
They have different initial points and extend in different directions.
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9. RAY CONT’D.
If C is between A and B, then 𝑪𝑨 and 𝑪𝑩 are opposite rays.
RECALL:
Points are collinear if they lie on the same line.
Similarly, segments and rays are collinear if they lie on the same plane.
So, any two opposite rays are collinear.
Segments, rays, and lines are coplanar if they lie on the same plane.
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10. EXAMPLE 1
Draw three non-collinear
points 𝐽, 𝐾, 𝐿.
Then draw
i. 𝐽𝐾
ii. 𝐾𝐿
iii. 𝐿𝐽
SOLUTION
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11. EXAMPLE 2
Draw two lines 𝑀𝑁 and
𝑃𝑄, that intersect at the
point 𝑋.
Use your diagram to
identify two pairs of
opposite rays.
SOLUTION
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The point 𝑋 is between 𝑀 𝑎𝑛𝑑 𝑁,
as well as 𝑃 𝑎𝑛𝑑 𝑄.
Therefore,
• 𝑋𝑀 𝑎𝑛𝑑 𝑋𝑁 are opposite rays.
• 𝑋𝑃 𝑎𝑛𝑑 𝑋𝑄 are opposite rays.

12. INTERSECTION OF
LINES AND PLANES
Two or more geometric figures intersect if they have one or
more points in common.
The intersection of the figures is the set of points they have in
common.
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13. EXAMPLE 3
SOLUTION
Sketch a line that intersects a plane at one
point.
Draw a plane and a line.
Emphasize the point where they meet.
Dashes indicate where the line is hidden by
the plane.
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14. EXAMPLE 4
SOLUTION
Sketch two planes that intersect in a line.
Draw two planes.
Emphasize the line where they meet.
Dashes indicate where one plane is hidden
by the other plane.
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15. THE END.
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