"Perpendicular Lines" Intersecting Lines and Parallel Lines PPT Courseware 3

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"Perpendicular Lines" Intersecting Lines and Parallel Lines PPT Courseware 3

Observe and think

In the model of intersecting lines, fix wooden bar a and rotate wooden bar b,

When the position of b changes, the angle α formed by a and b will also change.

1. Vertical definition: When one of the four angles formed by the intersection of two straight lines is a right angle, the two straight lines are perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and their intersection is called the vertical foot.

From the definition of perpendicular, we can see that the key to judging two straight lines to be perpendicular to each other is to find that one of the four intersection angles when the two straight lines intersect is a right angle.

2. Vertical representation:

1) Graphics:

2) Text: a and b are perpendicular to each other, and the vertical foot is O

3) Symbol: a⊥b or b⊥a. If you want to emphasize the vertical foot, record it as: a⊥b, and the vertical foot is O.

3. Vertical writing form:

As shown in the figure, when straight lines AB and CD intersect at point O, and ∠AOD=90°, AB⊥CD, the vertical foot is O.

Writing form:

①Judgment: ∵∠AOD=90° (known)

∴AB⊥CD (vertical definition)

On the contrary, if the straight line AB is perpendicular to CD and the vertical foot is O, then ∠AOD=90°.

Writing form:

②Properties: ∵ AB⊥CD (known)

∴ ∠AOD=90° (vertical definition)

(∠AOC=∠BOC=∠BOD=90°)

practice

Exercise 1. Among the four angles formed by the intersection of two straight lines, among the following conditions, it can be concluded that the two straight lines are perpendicular ( )

(A) There is an angle of 90° (B) There are two equal angles

(C) There are three angles that are equal. (D) There are four angles that are equal.

(E) There are four pairs of adjacent complementary angles (F) There are one pair of complementary pairs of vertex angles

(G) There is a pair of adjacent supplementary angles that are equal. (H) There are two sets of angles that are equal.

Think about it and do it

1. In primary school, we used origami to get two vertical lines. Now how many folding methods can you use to get two vertical lines?

2. As shown in Figure (5): There is a point A on the straight line a. After passing through the point A, how many straight lines can you make that are perpendicular to a? As shown in Figure (6): There is a point B outside the straight line a. After passing through the point B, how many straight lines can you make that are perpendicular to a?

Properties of vertical lines

Question: How many perpendicular lines to l can be drawn through the known straight line l and a point A on (or outside) l?

You can make one, and only one.

in conclusion:

There is only one straight line through a point that is perpendicular to the known straight line.

Notice:

Drawing a perpendicular to a known line segment (or ray) through a point is the perpendicular to the straight line where this line segment (or ray) is located.

1. Definition of vertical line

When one of the four angles formed by the intersection of two straight lines is a right angle, the two straight lines are perpendicular to each other. One of the straight lines is called the perpendicular to the other straight line, and their intersection is called the vertical foot.

2. How to draw vertical lines

1. Place; 2. Lean; 3. Move; 4. There is only one straight line perpendicular to the known straight line after drawing a point.

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Update Time: 2024-11-20

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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