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"Line Segments, Rays and Straight Lines" PPT Courseware 3
Experimentation and Inquiry(1)
Figure 1-25 shows high-voltage wires and several sparrows. If a wire is viewed as a straight line and a sparrow is viewed as a point, then how many positional relationships does a point have with a straight line?
The positional relationship between a point and a straight line
The point is on a straight line (the straight line passes through the point)
The point is outside the straight line (the straight line does not pass through the point)
Experimentation and Inquiry(2)
How many straight lines can be drawn past one point? How many straight lines can be drawn through two points? Give it a try.
An infinite number of straight lines can be drawn through a point. A straight line can and can only be drawn through two points, that is to say, two points determine a straight line.
Experimentation and Inquiry(3)
If two straight lines pass through the same point, they are said to intersect. At this time, the two straight lines have a unique common point. This common point is called their intersection point. In Figure 1-26, straight lines AB and CD intersect, and point O is their intersection.
Challenge yourself
Two straight lines on the plane can have at most one intersection point;
3 straight lines, with up to 3 intersection points;
4 straight lines, how many intersection points are there at most? Draw a picture.
If there are 5 straight lines on the plane, how many intersection points are there at most?
What patterns did you discover? Communicate with classmates.
n straight lines on the plane have at most _______ intersection points;
practise
1. Give practical examples of "two points determine a straight line" in life.
2. Draw a graph that meets the following requirements:
(1) Line AB passes through point C
(2) Point D is not on the straight line FE
(3) Straight lines a and b both pass through point G
(4) Straight lines m, n, l intersect with point p
3. As shown in the picture, fill in the blanks by looking at the picture:
(1) Point A is on the straight line BC_____.
(2) Point C is on ray BC_____.
(3) Point B is a _____ of line segment BC.
4. There are four points A, B, C, and D on the blackboard. Draw a straight line through every two points. Xiaoying said that 6 straight lines can be drawn. Xiaoliang said not necessarily. Tell us your opinions and communicate with your classmates. .
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