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Authoritative PPT Summary
"Intersecting Lines" PPT courseware
Part One: Observation and Thinking
As shown in the figure: Line AB and line CD intersect at point O
(1) What are the positional characteristics of ∠1 and ∠3 in the picture?
(2) What are the connections and differences between ∠1 and ∠3 on the edges and vertices in the figure?
Opposite top angle:
∠1 and ∠3 have a common vertex O, and the two sides are opposite extensions of each other. We call these two angles with special positions opposite vertex angles.
Intersecting lines PPT, the second part of the content: the eye of wisdom and knowledge
1.Are ∠1 and ∠2 opposite vertex angles? Why?
2. When light enters glass from the air, the propagation direction of the light changes: part of the light passes through the glass surface to form reflected light, and part of the light passes through the glass and is refracted, as shown in the figure. It is known from scientific experiments that ∠1=∠ 2, ∠4＜∠3, then are ∠1 and ∠2 opposite vertex angles? Are ∠3 and ∠4 opposite vertex angles? Why?
3. Please find all the opposite vertex angles in the picture
Answer: ∠2 and ∠6, ∠1 and ∠5, ∠3 and ∠4 are all related to the vertex angles
Intersection line PPT, the third part: experimental research
(1) Purpose of the activity: Explore the properties of opposite vertex angles.
(2) Activity steps:
1. Observe: when a straight line rotates around point O, the changes of ∠1 and ∠2.
2. Conjecture: The relationship between ∠1 and ∠2.
3. Discussion: Please use appropriate methods to verify your conjecture. How many methods do you have?
Are the opposite vertex angles equal?
It is known that the two straight lines intersect at point O.
Prove: ∠1=∠3 ∠2=∠4
prove:
Because ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary
So ∠1=∠3 (supplementary angles of the same angle are equal)
Similarly ∠2=∠4
Conclusion: Properties of opposite vertex angles: opposite vertex angles are equal
Intersecting lines PPT, part 4: do, do, practice
Please draw the corners that meet the following conditions based on the picture below:
⑴, and ∠ABC are opposite vertex angles;
⑵. It is the same angle as ∠ABC;
⑶, and ∠ABC are interior offset angles;
⑷, and ∠ABC are interior angles on the same side.
Fierce eyes and golden eyes
As shown on the right:
⑴. Point out the isotopic angle of ∠1;
⑵. Point out the interior angle of ∠2.
Isotropic angles: ∠1 and ∠CON, ∠1 and ∠EON
Internal offset angle: ∠2 and ∠NOF, ∠2 and ∠NOD
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