"Properties of Parallel Lines" PPT

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"Properties of Parallel Lines" PPT

Part One: Knowledge Review

1. If ∠B=∠1, AD//BC can be obtained according to ____________________

2. If ∠1=∠D, AB//CD can be obtained according to ____________________

3. If ∠B+∠BCD＝180, according to _______________, we can get_______________

4. If ∠2=∠4, according to _______________ we can get_______________

5. If _______=_______, based on the fact that the interior angles are equal and the two straight lines are parallel, we can get AB//CD

Properties of Parallel Lines PPT, Part 2: Properties of Parallel Lines

1. As shown in the figure, there are two straight lines a and b. If a//b is intercepted by a third straight line c, what are the characteristics of their co-position angles?

Two straight lines are parallel and have equal angles.

Characteristics of parallel lines

As shown in the figure, straight line a∥b,

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

Let’s talk

As shown in Figure 7-5-1, a//b are known, and they are intercepted by the third straight line c. According to the parallel line property theorem, we can get ∠1=∠5.

(1) From ∠1=∠5. Can it be deduced that ∠1 and ∠7 are equal? Are ∠2 and ∠8 also equal? Why?

(2) From ∠1=∠5. Can we deduce that two pairs of interior angles on the same side are complementary? Why?

As shown in Figure 7-5-2, AB∥CD, straight line AB, CD are intercepted by straight line EF, ∠1 and ∠2 are internal offset angles. The process of saying ∠1=∠2 is as follows:

Reason: ∵ AB∥CD ( )

∴ ∠1=∠3 ( )

∵ ∠2=∠3 ( )

∴∠1=∠2 ( )

Conclusion: Two straight lines are parallel and their internal offset angles are equal.

Nature of Parallel Lines PPT, Part 3: Classroom Problems

Have you learned it? give it a try

Question one:

1. If AD//BC, according to _______________________________, we can get ∠B=∠1

2. If AB//CD, according to _______________________________, we can get ∠D=∠1

3. If AD//BC, according to ______________, we can get ∠C＋_______=180

Question two:

1. If two straight lines are intercepted by a third straight line, then ( )

A． Equivalent angles are equal B. complementary angles

C. Interior angles on the same side are equal D. None of the above conclusions are correct

2. The angle bisectors of two parallel lines intercepted by a third straight line are perpendicular to each other ( )

A． Internal staggered angle B. Isotopic angle

C. Same side interior angle D. None of the above conclusions are correct

Question three:

Example 1: As shown in the figure, AD∥BC, AB∥DC, ∠1=100°, find the degrees of ∠2 and ∠3

Solution: Because AD∥BC

So ∠1=∠2 (the two straight lines are parallel and the internal offset angles are equal).

Because ∠1=100° (known)

So ∠2=100°

Because AB∥CD,

So ∠1+∠3=180° (two straight lines are parallel, and interior angles on the same side are complementary).

Because ∠1=100° (known),

So ∠3=180°-100°=80°.

PPT on the properties of parallel lines, part 4: practice in class

1. As shown in the figure, after two turns on a road, the direction is the same as the original direction, that is, the two roads before and after the turn are parallel to each other. The angle ∠B of the first turn is equal to 1420. What is the angle ∠C of the second turn? Why?

2. As shown in the figure, straight line DE passes through point A, DE//BC, ∠B=440, ∠C=570.

(1) What degree is ∠DAB equal to? Why?

(2) How many degrees is ∠DAC? Why?

Exercise: Known: As shown in the figure, ∠ADE=600, ∠B=600, ∠C=800.

Question ∠ How many degrees does AED equal? Why?

Solution: ∵ ∠ADE=∠B=600 (known)

∴ DE//BC (the parallel angles are equal and the two straight lines are parallel).

∴ ∠AED=∠C=800 (the two straight lines are parallel and have equal angles).

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