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"Properties of Parallel Lines" Intersecting Lines and Parallel Lines PPT Download (Lesson 1)
Part 1: Think about it
How to determine if two straight lines are parallel:
condition
Same angles
Internal angles are equal
Interior angles on same side are complementary
in conclusion
Two straight lines are parallel
PPT on the nature of parallel lines, part 2: discussion
As shown in the figure, line a is parallel to line b.
(1) Measure the sizes of the isotopic angles ∠1 and ∠5. What is their relationship? Are there any other isotropic angles in the picture? What does their size matter?
(2) How many pairs of internal offset angles are there in the picture? What does their size matter? Why?
(3) How many pairs of interior angles on the same side are there in the figure? What does their size matter? Why?
As shown in the figure, given a//b, are ∠4 and ∠5 equal? Why?
Solution: equal
∵a∥b (known),
∴∠1=∠5 (the two straight lines are parallel and have equal angles).
And ∵∠1=∠4 (the opposite vertex angles are equal),
∴ ∠4=∠5 (equivalent substitution).
As shown in the figure, given a//b, what is the relationship between ∠3 and ∠5? Why?
Solution: complementary
∵a//b (known),
∴∠1=∠5 (the two straight lines are parallel and have equal angles).
∵∠1+∠3=180° (supplementary angle definition),
∴∠3+∠5=180° (equivalent substitution).
Properties of parallel lines:
1. Two parallel straight lines are intercepted by a third straight line, and their co-position angles are equal.
Abbreviated as: Two straight lines are parallel and have equal angles.
2. Two parallel straight lines are intercepted by a third straight line, and their internal offset angles are equal.
Abbreviated as: Two straight lines are parallel and have equal angles.
3. Two parallel straight lines are intercepted by a third straight line, and the interior angles on the same side are complementary.
Abbreviated as: Two straight lines are parallel and the interior angles on the same side are complementary.
PPT on the properties of parallel lines, part 3: practice in class
1. As shown in the figure, if AB∥DE and AC∥DF, please tell the quantitative relationship between ∠A and ∠D and explain the reason.
Solution: ∠A =∠D.
Reason: ∵AB∥DE( )
∴∠A=_______ (two straight lines are parallel and have equal angles)
∵AC∥DF( )
∴∠D=______ (two straight lines are parallel and have equal angles)
∴∠A=∠D (equivalent substitution)
2. As shown in the figure, if AB∥DF, DE∥BC, and ∠1=65°, can you tell the degrees of ∠2, ∠3, and ∠4? Why?
Solution: Yes. ∠2＝∠3＝115°, ∠4＝65°.
The reason is as follows: ∵DE∥BC (known),
∴∠4＝∠1＝65° (the two straight lines are parallel and the internal offset angles are equal),
∠2+∠1=180° (two straight lines are parallel, and interior angles on the same side are complementary).
∵∠1=65° (known),
∴∠2＝180°-∠1＝115°.
Also ∵DF∥AB (known),
∴∠3=∠2 (the two straight lines are parallel and have equal angles).
∴∠3=115° (equivalent substitution).
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