"Property Theorem and Determination Theorem of Parallel Lines" PPT courseware

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"Property Theorem and Determination Theorem of Parallel Lines" PPT courseware

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Memorize the property theorem and judgment theorem of parallel lines

Understand the reasoning process of the property theorem and determination theorem of parallel lines, and be able to use axioms to reason out theorems and inferences.

Master the basic format of reasoning and be able to fill in the correct reasons

basic facts

If two straight lines are intercepted by a third straight line, if their angles are equal, then the two straight lines are parallel. (The parallel angles are equal and the two straight lines are parallel.)

Theorem 1 of properties of parallel lines:

Two parallel lines intersected by a third straight line have equal angles. (Two straight lines are parallel and have equal angles)

Note: Property Theorem 1 does not need to be proved at this stage. It can be directly used as a conclusion in various proof problems.

Theorem 2 of properties of parallel lines:

Two parallel lines intersected by a third straight line have equal interior angles.

(Two straight lines are parallel and their internal offset angles are equal)

1. Point out the conditions and conclusions of the theorem, draw graphics, and write known and verified facts based on the graphics.

2. Talk about your proof idea and try to write down the proof process.

Known: As shown in the figure, the straight lines AB∥CD, AB, CD are intercepted by the straight line EF, and ∠1 and ∠2 are internal offset angles.

Prove: ∠1 =∠2.

Proof: ∵AB∥CD (known),

∴∠1 =∠3 (the two straight lines are parallel and have equal angles).

∵∠2 =∠3 (the two vertex angles are equal),

∴∠1 =∠2 (equivalent substitution).

Determination of parallel lines?

axiom:

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

∵ ∠1=∠2, ∴ a∥b.

Decision theorem 1:

The internal angles are equal and the 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.

The conclusions here can be directly applied in the future.

Can you tell the converse of the following proposition? Are their converse propositions true or false?

(1) Two parallel lines are intercepted by a third straight line, and the interior angles on the same side are complementary.

(2) The opposite vertex angles are equal.

(3) Two parallel lines are intercepted by a third straight line, and their internal offset angles are equal.

Note: First determine the conditions and conclusion of the proposition, and then determine the converse proposition.

Known: As shown in the figure, DE ∥BC, ∠ADE=55 °, ∠C=54 °, find the degrees of ∠B and ∠DEC

Note: In future proof questions, the brackets and the basis in the brackets do not need to be written.

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Update Time: 2024-08-16

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 1 industry PPT template

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