"Determination of Parallelograms" Quadrilateral PPT Courseware 2

Description

"Determination of Parallelograms" Quadrilateral PPT Courseware 2

1. Knowledge goals:

1. After experiencing and understanding the process of exploring methods to identify parallelograms, we can gradually master the basic methods of reasoning.

2. Explore and understand how to identify parallelograms: a quadrilateral with two diagonals that bisect each other is a parallelogram; a set of parallelograms with opposite sides that are parallel and equal is a parallelogram. Relevant applications can be carried out based on the discrimination method.

2. Capability goals:

In the process of exploration, we develop our sense of reasonable reasoning and the habit of active inquiry.

3. Moral education goals:

Experiential mathematics activities come from life and serve life, improving our interest in learning.

We know the properties of parallelograms, so what methods can we use to determine whether a quadrilateral is a parallelogram?

(1) According to the definition: a quadrilateral with two sets of opposite sides that are parallel is called a parallelogram.

Because AB//CD,AD//BC;

So quadrilateral ABCD is a parallelogram.

A quadrilateral with two equal sides is a parallelogram.

Symbolic language:

∵AB=CD,AD=BC

∴ Quadrilateral ABCD is a parallelogram

Known: In quadrilateral ABCD, _________,

Prove: Quadrilateral ABCD is a parallelogram

Known: Quadrilateral ABCD, ∠A=∠C, ∠B=∠D

Prove: Quadrilateral ABCD is a parallelogram

Proof: ∵∠A=∠C, ∠B=∠D (known)

Also ∵∠A+ ∠B+ ∠C+ ∠D =360°

∴ 2∠A+ 2∠B=360°

That is ∠A+ ∠B=180°

∴ AD∥BC (interior angles on the same side are complementary, two straight lines are parallel)

Similarly, it can be proved that AB∥CD

∴ Quadrilateral ABCD is a parallelogram (a quadrilateral with two sets of opposite sides that are parallel is a parallelogram)

How to determine parallelograms

Judging from the edge

1. A quadrilateral with two sets of opposite sides that are parallel is a parallelogram.

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

3. 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

Show off your skills

1. It is known that: E and F are two points on the diagonal AC of the parallelogram ABCD, and AE=CF.

Prove: Quadrilateral BFDE is a parallelogram

Proof 2: Draw diagonal line BD and intersect AC at point O.

∵ Quadrilateral ABCD is a parallelogram

∴AO=CO，BO=DO

∵AE=CF

∴AO-AE=CO-CF

∴EO=FO

Also BO=DO

∴ Quadrilateral BFDE is a parallelogram

2. Known: As shown in the figure, E and F are the midpoints of sides AD and BC respectively.

Prove: BE=DF.

Prove: ∵ Quadrilateral ABCD is a parallelogram,

∴AB∥CD (definition of parallelogram)

AD=BC (opposite sides of a parallelogram are equal),

∵E and F are the midpoints of AD and BC respectively,

∴ED=BF, that is, ED∥�BF.

∴The quadrilateral EBFD is a parallelogram (a set of parallelograms with opposite sides that are parallel and equal is a parallelogram).

∴BE=DF (opposite sides of a parallelogram are equal).

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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:

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"Determination of Parallelograms" PPT download:

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"Determination of Parallelograms" PPT:

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Update Time: 2024-11-10

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