"Characteristics of Parallel Lines" Parallel Lines and Intersecting Lines PPT Courseware 2

Description

"Characteristics of Parallel Lines" Parallel Lines and Intersecting Lines PPT Courseware 2

Review & Thoughts

1. The angle formed by straight lines

Two straight lines intersect to form ____ angles. In terms of quantity, ∠1 and ∠2 form ____ angle. In terms of positional relationship, ∠2 and ∠4 form ____ angle; the two opposite angles_ ___.

2. Determine whether two straight lines are parallel

Co-position angle ____, two straight lines are parallel.

The internal offset angle is ____, and the two straight lines are parallel.

Same interior angle ____, two straight lines are parallel.

To examine whether two straight lines are parallel, we often use a third straight line as a bridge to connect the two straight lines——

Examine whether two angles that do not share the same vertex (among the eight angles cut by the third straight line) satisfy a certain quantitative relationship.

Grasping the two straight lines under investigation and looking for the third line; finding out the two angles with different vertices and their quantitative relationship is a necessary way to determine whether the two straight lines are parallel.

Do it

Find another set of parallel lines to illustrate your reasoning.

As shown in Figure 2-8, three identical triangle rulers form a figure. Please find a set of parallel lines in the figure and explain your reasons.

New knowledge exploration: What do you get when two straight lines are parallel?

As shown in the figure: Line a and line b are parallel.

(1) Measure the size of the isotropic angles ∠1 and ∠5. What is their relationship?

Are there any other isotropic angles in the picture?

What does their size matter?

(2) How many pairs of internal offset angles are there in the picture? What does their size matter? Why?

(3) How many pairs of interior angles on the same side are there in the figure? What does their size matter? Why?

Characteristics of two parallel straight lines

Rules: When two parallel straight lines are intercepted by a third straight line, the angles in the same direction are equal, the internal angles in the opposite direction are equal, and the internal angles on the same side are complementary.

Abbreviated as:

Two straight lines are parallel and have equal angles.

Two straight lines are parallel and their interior angles are equal.

Two straight lines are parallel and their interior angles on the same side are complementary.

Practice in class

1. As shown in the figure, AB∥CD, AC∥BD.

Find the angles that are equal or complementary to ∠1 respectively.

Solution: As shown in the figure, the angles equal to ∠1 are:

∠3, ∠5, ∠7, ∠9, ∠11, ∠13, ∠15;

The angles complementary to ∠1 are:

∠2, ∠4, ∠6, ∠8, ∠10, ∠12, ∠14, ∠16;

summary

In this lesson, we learned the three properties of parallel lines and summarized the differences between the determination and properties of parallel lines.

One of the keys here is to figure out what is "known" and what kind of "conclusion" is obtained. This ensures correct application and no errors.

In this lesson, you have initially learned how to use the judgment and properties of parallel lines to perform calculations and reasoning (proof).

To understand calculations in geometry, you often need to reason, and you must be familiar with the format of calculation problems in geometry;

You must also understand that in geometry, a series of new conclusions can often be derived from "known" conditions. In this process, you must be able to clearly understand the basis for each step of reasoning, and have a preliminary understanding of the format and requirements for answering such questions.

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Update Time: 2024-09-08

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