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

Description

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

As shown in the figure, line a is parallel to line b.

(1) Measure the isotropic angles ∠1 and ∠5. What is their relationship? Are there other isotopic angles? How are their sizes related?

(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?

What can you think of from this?

What can you think of from this?

When two parallel straight lines are intercepted by a third straight line, their concentric angles are equal, their interior angles are equal, and their interior angles on the same side are complementary.

abbreviation

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 the interior angles on the same side are complementary

Notice:

Only under the condition that two straight lines are parallel: the same angles and internal angles are equal, and the internal angles on the same side are complementary. Not all congruent angles and interior angles are equal. All interior angles on the same side are complementary.

practice

As shown in the figure, it is known that straight lines a and b are intercepted by straight line c. Fill in the appropriate basis for the reasoning in the following questions in the brackets:

(1)∵a∥b，∴ ∠1=∠3 ( )

(2)∵∠1=∠3, ∴ a∥b ( )

(3)∵a∥b，∴ ∠1=∠2 ( )

(4)∵a∥b，∴ ∠1+∠4=180°( )

(5)∵∠1=∠2 ,∴ a∥b ( )

(5)∵∠1=∠2 ,∴ a∥b ( )

Do it

As shown in the figure: a beam of parallel light rays AB and DE is reflected after hitting a horizontal mirror. At this time, ∠1=∠2 and ∠3=∠4.

(1) What is the relationship between the sizes of ∠1 and ∠3? What about ∠2 and ∠4?

Equal: ∠1=∠3;

∠2 =∠4.

(2) Are the reflected rays BC and EF also parallel? parallel

∵∠2=∠4 ∴BC∥EF.

Summary of this lesson

Characteristics of parallel lines

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.

Conditions for straight lines to be parallel

The parallel angles are equal and the two straight lines are parallel.

The internal angles are equal and the two straight lines are parallel.

Interior angles on the same side are complementary and two straight lines are parallel.

Expanded inquiry: If two parallel straight lines are intercepted by a third straight line, what is the positional relationship between a pair of angle bisectors with the same angle? What is the positional relationship between the angle bisectors of interior angles and the angle bisectors of interior angles on the same side?

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Update Time: 2024-10-01

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