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"Parallel Lines" Intersecting Lines and Parallel Lines PPT Courseware
Definition of parallel lines: Two straight lines that do not intersect in the same plane are called parallel lines.
What did you find?
Please use a ruler to draw two straight lines on the notebook. How many positions are there?
Discovery: There are two positional relationships, one is intersection and the other is parallel.
test you:
Can you draw parallel lines?
Given a straight line a and a known point P outside the straight line, draw a straight line through point P parallel to the known straight line a.
Parallel axiom corollary:
If two straight lines are parallel to a third straight line, then the two straight lines are also parallel to each other.
∵ b∥a b ∥ c
∴ a ∥c
Parallel lines are transitive.
Practice this:
1. Judge whether it is right or wrong (mark “√” if it is true, “×” if it is wrong)
1. Two straight lines that do not intersect are called parallel lines.
2. Two straight lines in the same plane intersect unless they are parallel.
3. There is only one parallel line to a straight line
4. After a point, there is and is only one straight line parallel to this straight line.
5.a, b, c are three straight lines. If a∥b and b∥c, then a∥c
2. In the same plane, straight lines a and b satisfy the following conditions
1. If a and b have no common points, then the positional relationship between a and b is _parallel_.
2. If a and b have one and only one common point, then the positional relationship between a and b _intersects_.
3. If AB∥CD and AB∥EF, then _CD_∥_EF_, the reason is ___parallel axiom inference___;
3. Which of the following statements is correct ( )
A. In the same plane, the positional relationships of two straight lines are intersection, perpendicular, and parallel.
B. If two line segments do not intersect in the same plane, then the two line segments are parallel.
C. In the same plane, two rays that do not intersect are parallel lines.
D. In the same plane, two straight lines that do not intersect are parallel lines.
summary:
1. Definition of parallel lines: Two straight lines that do not intersect in the same plane are called parallel lines.
2. Representation of parallel lines: Usually the symbol "//" is used to indicate parallel. AB//CD or a//b
3. Two properties of parallel lines:
①Parallel Axiom: (Uniqueness)
In the plane, through a point outside the straight line, there is one and only one straight line parallel to this straight line.
② Corollary: If two straight lines are parallel to a third straight line, then these two straight lines are also parallel to each other.
(Transitivity of parallel lines) If a//c,b//c; then a//b
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"Properties of Parallel Lines" PPT download:
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"Properties of Parallel Lines" PPT:
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