"Determination of Parallel Lines" PPT download

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"Determination of Parallel Lines" PPT download

Part One: Creation Issues

We already know that the same angles are equal and the two straight lines are parallel. That is, in the figure, if ∠1=∠2, then AB∥CD.

Application: ∵ ∠1=∠2, (known)

∴ AB∥CD (the angles are equal and the two straight lines are parallel)

creation problem

As shown in the figure, straight lines AB and CD are intercepted by straight line EF, ∠1=70°. If you add the condition __________, (just fill in one of the corners marked in the figure), you can get AB∥CD.

Think about it:

① Can you explain the reason for filling in this way?

②Is there any other way to fill in the form?

Communication: ①What conditions did the students in your group fill out?

②Why fill it out like this?

③Can I get AB∥CD after filling it in? Please explain why.

Judgment of Parallel Lines PPT, Part 2: Consolidation Practice

Consolidation exercise 1

Complete the following reasoning process. As shown in the figure, straight lines CD and EF are intercepted by straight line AB.

(1) ∵∠1=∠2 (known),

∴CD∥EF (equal angles, two straight lines are parallel)

(2) ∵ ∠2 = ∠3, (known)

∴CD∥EF (the internal offset angles are equal and the two straight lines are parallel)

(3) ∠2 + ∠4 =180° (known)

∴CD∥EF (interior angles on the same side are complementary and two straight lines are parallel)

Consolidation Exercise 2

As shown in the figure, it is known that straight lines AB and CD are intercepted by straight line EF, ∠1=60°, ∠2=120°.

Give reasons for AB∥CD.

Consolidation exercise 3

As shown in the figure, the condition for obtaining DE∥BC is ( )

A. ∠Ｃ＝∠ＢＡＣ

B. ∠ABC＋∠BAE＝180°

C. ∠Ｃ＋＋∠ＢＡＤ＝180°

D． ∠Ｃ＝∠ＢＡＤ

Judgment of parallel lines PPT, part three: summary of what has been learned

Let’s talk about what new knowledge we explored in this class? What are they used for? What should you pay attention to when applying?

The methods to determine whether two straight lines are parallel are:

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.

When judging that two straight lines are parallel, you must clearly see which two straight lines are intercepted by the third straight line and form equal angles of the same position, equal interior angles, and complementary internal angles on the same side, so that you can correctly determine which two straight lines are parallel.

Judgment of Parallel Lines PPT, Part 4: Classroom Test

① ∵∠B＝∠EAD (known),

∴AD∥BC (the angles are equal and the two straight lines are parallel);

② ∵∠Ｄ＝∠ＥＡＤ (known),

∴BE∥CD (the internal offset angles are equal and the two straight lines are parallel);

③ ∵ ∠B+∠BCD=180° (known),

∴AB∥CD (the interior angles on the same side are complementary and the two straight lines are parallel).

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Update Time: 2024-07-01

This template belongs to Mathematics courseware Hebei Education Edition Seventh Grade Mathematics Volume 2 industry PPT template

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