"If Two Straight Lines Are Parallel" Proof PPT Courseware 3

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"If Two Straight Lines Are Parallel" Proof PPT Courseware 3

Judgment of parallel lines

Axiom: The angles of the same angle are equal and the two straight lines are parallel.

∵ ∠1=∠2, ∴ a∥b.

Determination Theorem 1: Internal angles are equal and two straight lines are parallel.

∵ ∠1=∠2, ∴ a∥b.

Decision Theorem 2: Interior angles on the same side are complementary and two straight lines are parallel.

∵∠1+∠2=1800, ∴ a∥b.

Think about it:

(1) According to "two parallel lines are intercepted by a third straight line, and the internal offset angles are equal." Can you make related graphics?

(2) Can you write down what you know and verify based on the graph you made?

(3) Can you talk about the idea of ​​​​the proof?

It is known that, as shown in the figure, straight lines a//b, ∠1 and ∠2 are the intersecting angles of straight lines a and b intercepted by straight line c.

Prove: ∠1＝∠2

Proof: ∵a∥b (known)

∴∠3=∠2 (two straight lines are parallel and have equal angles)

∵ ∠3=∠1 (the two vertex angles are equal)

∴∠1=∠2 (equivalent substitution)

Do it

Known: As shown in the figure, straight lines a//b, ∠1 and ∠2 are interior angles on the same side of straight lines a and b intercepted by straight line c.

Prove: ∠1+∠2＝180°

Proof method 1: a//b (known)

∠3=∠2 (the two straight lines are parallel and have equal angles)

∠1+∠3=180° (1 straight angle=180°)

∠1+∠2＝180° (equivalent substitution)

Proof method 2: a//b (known)

∠3=∠2 (the two straight lines are parallel and the internal offset angles are equal)

∠1+∠3=180° (1 straight angle=180°)

∠1+∠2＝180° (equivalent substitution)

General steps for proof:

Step 1: Draw the graph according to the meaning of the question.

First, draw a graph based on the conditions of the proposition, that is, the known matters, and then mark the conclusion of the proposition, that is, the need for verification, with the necessary letters or symbols on the graph to facilitate the expression of the narrative or reasoning process.

Step 2: Based on the conditions, conclusions, and combined graphics, write down what is known and verify it.

The condition of the proposition into the language of geometric symbols is written in Known, and the conclusion of the proposition into the language of geometric symbols is written in Verification.

Step 3: After analysis, find out the way to prove from what is known, and write down the proof process.

Under normal circumstances, the analysis process is not required to be written down. In some questions, the graph has been drawn, the known information has been written, and the verification is required. At this time, you only need to write the "proof" item.

According to the following propositions, draw the graph, and combine the graph to write the known and verified (do not write the proof process):

1) Two straight lines perpendicular to the same straight line are parallel;

Known: straight line b⊥a, c⊥a

Prove: b∥c

2) The distance from a point on the bisector of an angle to both sides of the angle is equal;

Known: As shown in the figure, OC is the bisector of ∠AOB,

EF⊥OA in F ,

EG⊥OB in G

Prove: EF=EG

3) If two straight lines are parallel to a third straight line, then the two straight lines are also parallel to each other.

Known: As shown in the figure, straight lines a, b, c are bounded by straight line d

Cut off, and a∥b,c∥b,

Prove: a∥c

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"If Two Straight Lines Are Parallel" Proof PPT Courseware 1 According to the fact that two parallel lines are intercepted by a third straight line, the internal offset angles are equal. Can you make related figures? 2. Can you write down what you know and verify based on the graph you made? 3 Can you explain the idea of ​​​​the proof? Two known...

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Update Time: 2024-10-20

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