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"Properties of Parallel Lines" PPT courseware
Review and Thoughts
As shown in the figure of "Three Lines and Eight Angles", find all the same angles, interior angles, and interior angles on the same side (pay attention to distinguish their positional characteristics).
If the straight lines a and b in the figure are two parallel straight lines, what is the quantitative relationship between the congruent angles, interior angles, and interior angles on the same side?
learning target:
1. Explore the properties of parallel lines and be able to express their properties using literal language and symbolic language.
2. Able to use properties for reasoning and calculation.
3. Understand the concept of distance between parallel lines.
property discovery
Properties of parallel lines 1
Two parallel lines intersected by a third straight line have equal angles.
The abbreviation is: two straight lines are parallel and have equal angles.
Symbolic language: Because a∥b, so ∠1=∠5.
Properties of parallel lines 2
Two parallel lines are intercepted by a third straight line, and their interior angles are equal.
The abbreviation is: two straight lines are parallel and their internal offset angles are equal.
Symbolic language: Because a∥b, so ∠3=∠5.
Properties of parallel lines 3
Two parallel lines are intercepted by a third straight line, and the interior angles on the same side are complementary.
The abbreviation is: two straight lines are parallel and the interior angles on the same side are complementary.
Symbolic language: Because a∥b, so ∠2+∠5=180°.
communication and discovery
Draw pictures as required:
(1) As shown in the figure, l1 and l2 are parallel. Pick a point A on l1 and draw the vertical line AC of l2 through point A. The vertical foot is C. Then is AC perpendicular to l1? Why?
(2) Take another point B on l1 and draw the vertical segment BD to l2 in the same way. Then what is the relationship between the positions and sizes of AC and BD? Why?
(3) Draw countless such vertical line segments, what can you find?
Think about it:
Today you learned about the distance between parallel lines, so can you measure the thickness of math textbooks? Communicate with your peers and see who comes up with the answer first.
Compliance in court
1. As shown in the figure: AB∥DE, ∠B=500, then ∠1= ∠2= ∠3= .
2. Write the reasoning process based on the graph on the right
Because AB∥CD (known)
So ∠1=∠___()
And because ∠3=∠2()
So ∠1=∠___ (equivalent substitution)
Because ∠4+∠2=___ (supplementary angle definition)
So ∠4+∠___=180° (equivalent substitution)
Homework assignment
Required questions: Questions 1 and 3 of Exercise 9.3 on page 37 of the textbook.
Optional question: Questions 4 and 5 of Exercise 9.3 on page 37 of the textbook.
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"Properties of Parallel Lines" PPT download:
"Properties of Parallel Lines" PPT Download Part 1 Content: Review Review What are the methods for determining parallel lines? How to identify parallel lines: (1) the angles of the same angles are equal, two straight lines are parallel (2) the internal angles are equal, the two straight lines are parallel (3) the internal angles on the same side are complementary, Two straight lines are parallel...
"Properties of Parallel Lines" PPT:
"Properties of Parallel Lines" PPT Part One Content: Knowledge Review 1. If B=1, according to _______________, we can get AD//BC 2. If 1=D, according to _______________, we can get AB//CD 3. If B+BCD=180, according to___..
"Properties of Parallel Lines" PPT courseware download:
"Properties of Parallel Lines" PPT courseware download Part 1 content: Do a hands-on experiment: Select any two parallel lines a, b on the prepared grid book (1) Draw a straight line c and parallel lines a, b arbitrarily intersect. (2) Choose any pair of co-positioned angles and measure them with a protractor...