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Authoritative PPT Summary
"The Property Theorem and Determination Theorem of Parallel Lines" PPT Courseware 3
Knowledge review:
(1) What is a proposition? How many categories can propositions be divided into?
(2) What parts does a proposition consist of?
(3) What is the general narrative form of propositions?
Let’s talk
If two angles are right angles, then the two angles are equal.
If two angles are equal, then they are right angles.
If a and b are opposites of each other, then a+b=0.
If a+b=0, then a and b are opposite numbers of each other.
reciprocal proposition
Among two propositions, if the condition of the first proposition is the conclusion of the second proposition and the conclusion of the first proposition is the condition of the second proposition, then the two propositions are called reciprocal propositions.
The internal angles are equal and the two straight lines are parallel.
Two straight lines are parallel and their internal offset angles are equal.
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) If two triangles are congruent, then the corresponding sides are equal.
Note: First determine the conditions and conclusion of the proposition, and then determine the converse proposition.
Thinking: If a proposition is a true proposition, then must its converse proposition be correct?
The converse of a true proposition is not necessarily a true proposition
Think: Are all true propositions theorems? Do all theorems have their converses?
Only some of the true propositions are called theorems
Only theorems whose converse proposition is correct have a converse proposition
Converse Theorem If the converse of a theorem is true, then the converse is the converse of the original theorem.
Theorem 1 of properties of parallel lines:
Two parallel lines intersected by a third straight line have equal angles.
Theorem 2 of properties of parallel lines:
Two parallel lines intersected by a third straight line have equal interior angles.
Theorem 3 of properties of parallel lines:
Two parallel lines are intercepted by a third straight line, and their interior angles are complementary.
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.
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.
Parallel Line Determination Theorem 1:
If two straight lines are intercepted by a third straight line, if the internal offset angles are equal, then the two straight lines are parallel.
Parallel Line Determination Theorem 2:
Two straight lines are intercepted by a third straight line. If the interior angles on the same side are complementary, then the two straight lines are parallel.
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"Property Theorem and Determination Theorem of Parallel Lines" PPT Courseware 2:
"The Property Theorem and Judgment Theorem of Parallel Lines" PPT Courseware 2 Review: The Judgment Theorem of Parallel Lines and Planes If a straight line outside a plane is parallel to a straight line in this plane, then this straight line is parallel to this plane. Note: 1. The three conditions of the theorem are indispensable..
"Property Theorem and Determination Theorem of Parallel Lines" PPT courseware:
"The Property Theorem and Determination Theorem of Parallel Lines" PPT Courseware Objective Click Memorize the property theorem and decision theorem of parallel lines Understand the reasoning process of the property theorem and decision theorem of parallel lines, and be able to use axioms to reason out theorems and inferences. Master the basic format of reasoning,...