"Determination of Parallelograms" PPT download

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"Determination of Parallelograms" PPT download

Part One: Learning Objectives

1. Understand and master the determination theorem of parallelograms

2. Master the application of judgment theorem to explain the judgment of parallelogram.

3. Develop reasoning awareness during activities and gradually master the basic methods of reasoning.

Key Points Determination Theorem of Parallelograms

Difficulty: Comprehensive application of properties and determination of parallelograms

Judgment of parallelograms PPT, part 2: knowledge exploration

Think based on the properties of parallelograms: Is a quadrilateral with equal opposite sides or equal angles or equal diagonals bisecting each other a parallelogram?

As shown in the picture, four thin wooden strips, two long and two short, are twisted together with small nails to form a quadrilateral, so that the equal-length wooden strips become opposite sides. Rotate this quadrilateral and change its shape. During the process of changing the shape, is it always a parallelogram?

can be discovered by exploring

Although the shape of the wooden bar changes during the rotation process, it is always a parallelogram.

From this we can guess:

Two sets of opposite sides are equal

A quadrilateral is a parallelogram.

Can you verify your conjecture with a geometric proof?

PPT on the determination of parallelograms, part three: verification of theorem

The correctness of the conjecture is verified through proof, so we get the determination theorem 1 of parallelogram:

A quadrilateral with two equal sides is a parallelogram.

Mathematical language representation:

∵AB=CD, AD=BC (known)

∴ Quadrilateral ABCD is a parallelogram

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

Through the proof, we get the Determination Theorem 2 of parallelogram:

A quadrilateral whose diagonals bisect each other is a parallelogram.

Mathematical language representation:

∵ OA=OC, OB=OD (known)

∴ Quadrilateral ABCD is a parallelogram

(A quadrilateral whose diagonals bisect each other is a parallelogram)

Determination theorem 3 of parallelogram:

A quadrilateral with two equal opposite angles is a parallelogram.

Mathematical language representation:

∵∠A=∠C, ∠B=∠D (known)

∴ Quadrilateral ABCD is a parallelogram

(A quadrilateral with two equal opposite angles is a parallelogram)

Method 5 for determining parallelograms:

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

Mathematical language:

∵AB∥CD, AB＝CD

∴A quadrilateral is a parallelogram

Judgment of parallelograms PPT, part 4: Consolidation and improvement

Known: As shown in the figure: AB=CD, ∠DCA=∠BAC,

Question: Is quadrilateral ABCD a parallelogram?

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for eighth grade volume 2, PPT download on the determination of parallelograms, .PPT format;

For more information about the "Determination of Parallelograms" PPT courseware, please click on the "Determination of Parallelograms" ppt tab.

"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:

"Determination of Parallelograms" PPT Part 1 Content: Properties of parallelograms Sides: Opposite sides are parallel, opposite sides are equal Corollary: Parallel line segments sandwiched between two parallel lines are equal Angles: Opposite angles are equal, adjacent angles are complementary, four angles sum to 360 Diagonals: Bisect each other symmetrically..

"Determination of Parallelograms" PPT courseware 3:

"Determination of Parallelograms" PPT Courseware 3 Review What are the properties and determinations of parallelograms that we have learned before? Properties Opposite sides of a parallelogram are equal. Opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other. Determination: Two sets of opposite sides are parallel..

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Update Time: 2024-07-11

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