"Definition and Proposition" Proof of Parallel Lines PPT Courseware

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"Definition and Proposition" Proof of Parallel Lines PPT Courseware

It can be seen that communication must have a common understanding of certain names and terms to proceed.

To this end, it is necessary to describe and clearly define the meanings of names and terms, that is, to give their definitions.

For example:

"Persons with the nationality of the People's Republic of China are called citizens of the People's Republic of China" is the definition of "citizen of the People's Republic of China";

"The length of the line segment between two points is called the distance between the two points" is the definition of "the distance between two points";

"In an equation, there is only one unknown number, and the exponent of the unknown number is 1. Such an equation is called a linear equation of one variable" is the definition of "a linear equation of one variable";

"A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram" is the definition of "parallelogram";

practice

(1) Pandas have no wings;

(2) Any triangle must have right angles;

(3) The opposite vertex angles are equal;

(4) No matter what natural number n is, the value of the formula n2-n+11 is a prime number;

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

Propositions are generally written in the form of "if..., then...". Can you write the above propositions in the form of "if..., then..."?

On the other hand, if a sentence does not make any judgment about a certain thing, then it is not a proposition. For example, the following sentences are not propositions:

(1)Do you like mathematics?

(2)Construct line segment AB=CD.

Supplement: Determine which of the following statements are propositions? Which ones are not propositions?

(1) All right angles are equal.

(2) Two angles equal to the same angle are equal.

(3) Draw two equal line segments.

(4) On ray OA, pick any two points B and C.

(5) In space, two non-parallel straight lines must intersect.

(6) The bisectors of a pair of adjacent supplementary angles are perpendicular to each other.

(7) Extend line segment AB to C so that AC=2AB.

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

Observe the following propositions and guess the common structural features of these propositions. Communicate with your peers

(1) If the three sides of two triangles are equal, then the two triangles are congruent;

(2) If a set of opposite sides of a quadrilateral are parallel and equal, then the quadrilateral is a parallelogram;

(3) If a triangle is an isosceles triangle, then the two base angles of the triangle are equal;

(4) If the diagonals of a quadrilateral are equal, then the quadrilateral is a rectangle;

(5) If the two diagonals of a quadrilateral are perpendicular to each other, then the quadrilateral is a rhombus.

Every proposition consists of two parts: conditions and conclusions. Conditions are known matters, and conclusions are matters inferred from the already known matters.

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