"Intersecting Lines" Intersecting Lines and Parallel Lines PPT Courseware

Description

"Intersecting Lines" Intersecting Lines and Parallel Lines PPT Courseware

If two straight lines have only one common point, they are said to intersect.

This common point is called the intersection point of the two straight lines.

Lines AB and CD intersect at point O

think

Question 1: How many angles are formed when two straight lines intersect? Express it.

Question 2: What are the connections between ∠1 and ∠3 and ∠2 and ∠4 respectively?

The vertices are the same.

The two sides of the angle are opposite extensions of each other.

Two straight lines intersect to form an opposite angle

1. The vertices are the same.

2. The two sides of the angle are opposite extension lines of each other.

think

Question 1: How many angles are formed when two straight lines intersect? Express it.

Question 2: What are the connections between ∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1 respectively?

adjacent supplementary angle

1. There is a common edge

2. The other sides of the angle are reverse extension lines of each other.

The difference and relationship between adjacent supplementary angles and supplementary angles

1. Adjacent and supplementary angles are both for two angles, and the quantitative relationship is that the sum of the two angles is 180°.

2. Two angles that are complementary angles must be complementary, but two angles that are complementary angles are not necessarily complementary angles. That is: two complementary angles only focus on the quantitative relationship without talking about the position, but are complementary to each other. The two corners of an angle must satisfy both the quantity relationship and the positional relationship.

Think about it:

The measuring tool in the picture can measure the angle formed by the extension lines of the two contour lines AB and CD of the parts in the picture. Can you tell me the reason?

Variations

It is known that straight lines a and b intersect, 1=40 degrees, find the degrees of ∠2, ∠3 and ∠4.

Variation: Change ∠1=40 degrees to

∠2 is 3 times of ∠1, find ∠2,

The degree of ∠3, ∠4.

Comment: This problem can be solved with the help of equations. In geometry, problems such as calculating the size of angles or the length of line segments are often solved with the help of algebraic equations.

judge

(1) Vertex angles are equal ( )

(2) Congruent angles are opposite vertex angles ( )

(3) If two angles are not equal, they must not be opposite vertex angles. ( )

(4) If the two angles are not opposite vertex angles, then the two angles are not equal. ( )

(5) There are common vertices, and equal angles are opposite vertex angles ( )

(6) When two straight lines intersect, the angle with a common vertex is the opposite vertex angle ( )

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Update Time: 2024-11-20

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