"Determination of Parallelograms" Quadrilateral PPT courseware

Description

"Determination of Parallelograms" Quadrilateral PPT courseware

Main characteristics of parallelograms

1. Side: a. The two opposite sides of a parallelogram are parallel.

b. The two opposite sides of a parallelogram are equal.

2. Angles: The two opposite angles of a parallelogram are equal.

3． Diagonals: The diagonals of a parallelogram bisect each other.

teaching objectives

【Knowledge and Ability】

Systematically master the determination theorem of parallelograms;

Flexibly use judgment theorems to make relevant judgments and reasoning narratives.

【Process and Method】

Through the induction and reasoning of the parallelogram determination theorem, cultivate inductive reasoning ability and understand the rigor of mathematics;

Cultivate the ability to analyze and solve problems through trial exercises and variant attempts.

[Emotional attitudes and values]

Through the flexible use of parallelogram determination methods, cultivate the spirit of active exploration and innovation consciousness;

Through one question with multiple variations and one question with multiple solutions, it arouses the desire for diversity and innovation.

The above issues can be summarized as:

Known: In the quadrilateral ABCD, AB=CD, AD=BC.

Prove: Quadrilateral ABCD is a parallelogram.

Proof: Connect AC.

∵ AB=CD, AD=BC, AC=AC

∴△ACD≌△CAD (SSS)

∴∠CAB=∠DCA

∴AB∥CD

In the same way, ∠CAD = ∠ACB

∴AD∥BC

∴ Quadrilateral ABCD is a parallelogram.

Knowledge points

Parallelogram determination method 1

A quadrilateral with two sets of opposite sides equal to each other is a parallelogram.

Parallelogram Determination Method 2

A quadrilateral whose diagonals bisect each other is a parallelogram.

Determination theorem 3 of parallelogram:

A set of quadrilaterals whose opposite sides are parallel and equal is a parallelogram

Determination Theorem 4 of Parallelogram:

A quadrilateral with two equal opposite angles is a parallelogram.

small exercise

Known: As shown in the figure, A′B′∥BA, B′C′∥CB, C′A′∥AC.

Verify:

(1) ∠ABC=∠B′, ∠CAB=∠A′, ∠BCA=∠C′;

(2) The vertices of △ABC are the midpoints of each side of △B′C′A′.

Proof: (1) ∵ A′B′∥BA, C′B′∥BC,

∴ Quadrilateral ABCB′ is a parallelogram.

∴　∠ABC=∠B′ (opposite angles of a parallelogram are equal).

In the same way, ∠CAB=∠A′, ∠BCA=∠C′.

(2) From (1), it is proved that the quadrilateral ABCB′ is a parallelogram. In the same way, the quadrilateral ABA'C is a parallelogram.

∴ AB=B′C, AB=A′C (opposite sides of the parallelogram are equal).

∴ B′C＝A′C.

In the same way, B′A=C′A, A′B=C′B.

∴　The vertices A, B, and C of △ABC are the midpoints of the sides B′C′, C′A′, and A′B′ of △B′C′A′ respectively.

Class summary

How to determine parallelograms

Judging from the edge

A quadrilateral with two opposite sides that are parallel is a parallelogram

A quadrilateral with two equal sides is a parallelogram.

A set of quadrilaterals whose opposite sides are parallel and equal is a parallelogram

Judging from the angle

A quadrilateral with two equal opposite angles is a parallelogram

Judging from the diagonal

A quadrilateral with two diagonals that bisect each other is a parallelogram

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For more information about the "Determination of Parallelograms as Quadrilaterals" PPT courseware, please click on the "Determination of Parallelograms ppt Quadrilateral ppt" tag.

"Determination of Parallelograms" PPT courseware download:

"Determination of Parallelograms" PPT courseware download Part 1 content: Review Review: Briefly describe the properties of parallelograms: 1. The opposite sides of a parallelogram are equal 2. The diagonals of a parallelogram are equal 3. The diagonals of a parallelogram bisect each other 4. A parallelogram Opposite sides...

"Determination of Parallelograms" PPT download:

"Determination of Parallelograms" PPT Download Part One: Learning Objectives 1. Understand and master the determination theorem of parallelograms 2. Master the application of the determination theorem to explain the determination of parallelograms. 3. Develop reasoning awareness during activities and gradually master the skills of reasoning..

"Determination of Parallelograms" PPT:

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Update Time: 2024-11-19

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

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