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"Exploring the Conditions of Parallel Lines" Parallel Lines and Intersecting Lines PPT Courseware 3
Knowledge review
Question 1: What are the positional relationships between two straight lines in the same plane? What are the differences?
Question 2: As shown in the figure, what are the relationships between the four angles formed by the intersection of two straight lines?
Get to know the "Three Lines and Eight Anises":
Two straight lines are intercepted by a third straight line, forming a "three-line octagon". Angles with a positional relationship such as ∠1 and ∠2 are called homotopic angles.
∠1 and ∠2 are the same angles
∠3 and ∠4 are the same angles
∠5 and ∠6 are the same angles
∠7 and ∠8 are the same angles
Do you remember how to draw two parallel lines using a moving set square?
Draw a parallel line through a point outside the known straight line. Please explain the reason.
The parallel angles are equal and the two straight lines are parallel.
Migrate applications
1. The "Mathematical Understanding" column of the textbook shows us a tool for drawing parallel lines. Before drawing parallel lines, the master worker often has to adjust the tool first, and then draw parallel lines. Can you explain the use of this tool and the meaning of it? Does it make sense?
2. As shown in the figure, a beam DE is added to the roof truss. It is known that ∠B=32°. To make DE∥BC, how many degrees must ∠ADE equal? Why?
knowledge gas station
1. What are the characteristics of the angles in the figure with the positional relationship between ∠3 and ∠5, and ∠4 and ∠6? Tell us your reasons.
The angles with such positional relationships as ∠3 and ∠5, ∠4 and ∠6, are staggered inside the two intercepted straight lines and on both sides of the intercepted lines. Such angles are called internal offset angles.
2. What about angles with such positional relationships as ∠3 and ∠6, and ∠4 and ∠5? Tell us your reasons.
The angles with the positional relationship of ∠3 and ∠6, ∠4 and ∠5 are inside the two intercepted lines and on the same side of the intercepting lines. Such angles are called interior angles on the same side.
independent inquiry
Try it: Can you use three triangular plates of the same size (30°, 60°, 90°) to form a figure containing parallel line segments? Give it a try and put together a few more figures. After finding the parallel line segments, explain Your reasons.
practice
1. When each angle in the figure meets the following conditions, can you determine which two straight lines are parallel?
(1)∠1＝∠4; (2)∠2＝∠4; (3)∠1+∠3=180°
2. Look at the picture and fill in the blanks: As shown in the picture on the right, ∵∠1=∠2
∴AC∥AE,
∵∠2＝∠4
∴ DE∥FG, the parallel angles are equal and the two straight lines are parallel
∴AC∥FG.
Conditions for two straight lines to be parallel (judgment of parallel lines)
① The parallel angles are equal and the two straight lines are parallel;
② The internal offset angles are equal and the two straight lines are parallel;
③ Interior angles on the same side are complementary and two straight lines are parallel.
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For more information about the PPT courseware "Parallel Lines and Intersecting Lines Exploring the Conditions of Parallel Lines", please click the "Parallel Lines and Intersecting Lines ppt Exploring the Conditions of Parallel Straight Lines" ppt tag.
"Exploring the Conditions for Parallel Lines" PPT Courseware of Parallel Lines and Intersecting Lines 2:
"Exploring the Conditions of Parallel Lines" Parallel Lines and Intersecting Lines PPT Courseware 2 Exploring the Conditions of Parallel Lines The decoration worker is nailing wooden strips to the wall. If wooden strip b is perpendicular to the edge of the wall, then wooden strip a is sandwiched between the edge of the wall and the edge of the wall. At what angle can the wooden bar be made a...
"Exploring the Conditions of Parallel Lines" PPT Courseware of Parallel Lines and Intersecting Lines:
"Exploring the Conditions for Parallel Straight Lines" Parallel Lines and Intersecting Lines PPT courseware Methods that can be used to determine the conditions for two straight lines to be parallel 1. Parallel definition 2. Parallel axiom corollary 3. Two straight lines with equal angles are parallel to each other. Two straight lines AB and CD are parallel to each other. EF intercepts and observes the positions of 3 and 5..