"Supplementary Angle and Supplementary Angle" Parallel Lines and Intersecting Lines PPT Courseware

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"Supplementary Angle and Supplementary Angle" Parallel Lines and Intersecting Lines PPT Courseware

As shown in the picture, when playing billiards, choose the appropriate direction to hit the red ball with the white ball. The red ball will go directly into the bag after rebounding. At this time, ∠1 is equal to ∠2.

Which angles are supplementary angles?

Supplementary angles and supplementary angles are the relationship between two angles. Like a pair of opposite numbers, they are relative to each other. For example, if 1 and -1 are opposites of each other, the opposite of 1 is -1, and the opposite of -1 is 1.

Supplementary angles and supplementary angles have nothing to do with the position of the angle, only their number.

①If an angle is 60°, its supplementary angle is _______;

②If an acute angle is X, then its complementary angle is _______;

③If an angle is 60°, its supplementary angle is _______;

④If an angle is X, then its supplementary angle is _______;

As shown in Figure (1), what kind of angles are ∠1 and ∠2? (where ∠3 is a right angle)

As shown in Figure (2), what kind of angles are ∠1 and ∠2?

As shown in Figure (3), what kind of angles are ∠1 and ∠2? What about ∠3 and ∠4? (where ∠3 and ∠4 are right angles)

Think about the properties of complementary and supplementary angles

1. It is known that ON⊥DE , 1= 2, try to answer the following questions:

(1) Which angles are supplementary angles? Which angles are supplementary to each other?

(2) What is the relationship between ∠3 and ∠4? Why?

(3) What is the relationship between ∠AOE and ∠BOD? Why?

Thought questions:

1. An angle is three times its supplementary angle. What is the degree of this angle?

2. An angle is 20° smaller than its supplementary angle. What is its supplementary angle?

Compare: see who is faster

Solving geometric problems using algebraic methods is a common strategy.

Solution: Assume ∠4 =x, then ∠1=2x

∵∠1+∠DOE+∠4=1800

∴2x＋90°＋x＝180°

The solution is x=30°, that is, ∠4=30°

Also ∵∠2＋∠COE＝90° ∠4＋∠COE＝90

∴∠2=∠3 (Supplementary angles of the same angle are equal)

∴∠2= 30°

Discuss about the vertex angle and its properties

(1) When cutting something with scissors, which pair of corners becomes larger or smaller at the same time?

(2) If Figure 2-2 is simply represented as Figure 2-3, what is the relationship between the positions of ∠1 and ∠2? What does their size matter?

Introducing the concept: As shown in Figure 2-3, straight lines AB and CD intersect at point O,

∠1 and ∠2 have a common vertex, and their two sides are opposite extensions of each other. Such two angles are called opposite vertex angles.

Vertical angles are equal

Note: (1) An angle has only one opposite vertex angle,

(2) To master the concept of vertex angle, you should pay attention to three points:

1° is obtained by the intersection of two straight lines; 2° has a common vertex; 3° has no common edges, and all three conditions are indispensable.

Knowledge sorting

If the sum of two angles is a right angle, then the two angles are said to be _____ to each other;

The two angles of _______________ are called supplementary angles;

Supplementary angles and supplementary angles are the relationship between two angles.

Supplementary angles and supplementary angles have nothing to do with the angle _____, only with its _____.

The supplementary angles of _______________ are equal, and the supplementary angles of _______________ are equal;

Two angles with a common vertex and opposite extensions of each other are called _____.

Among the four angles formed by the intersection of two straight lines, there are _____ opposite vertex angles.

Opposite top angle _____.

I have gained a lot and still need to be able to sort it out!

Summary: What content, methods, and issues should be paid attention to in this lesson?

Concepts learned? 1. Complementary angles; 2. Supplementary angles; 3. Opposite angles.

What is the nature of what is learned? 1. The supplementary angles of the same angle or equal angles are equal; 2. The supplementary angles of the same angle or equal angles are equal; 3. The opposite vertex angles are equal.

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For more information about the "Parallel Lines and Intersecting Lines Complementary and Supplementary Angle" PPT courseware, please click on the Parallel Lines and Intersecting Lines ppt Complementary and Supplementary Angle ppt tag.

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Update Time: 2024-10-06

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