"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

Difficulties 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.

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"Determination of Parallelograms" Parallelogram PPT download (Lesson 3), 21 pages in total. Learning objectives: Explore and prove the equality properties of parallel line segments sandwiched between parallel lines; use the equality properties of parallel line segments between parallel lines to solve related problems, and understand the equality between parallel lines..

"Determination of Parallelograms" Parallelogram PPT Download (Lesson 2):

"Determination of Parallelograms" Parallelogram PPT download (Lesson 2), 21 pages in total. Learning Objectives Explore and prove the determination theorem that a quadrilateral whose diagonals bisect each other is a parallelogram; use the determination that a quadrilateral whose diagonals bisect each other is a parallelogram..

"Determination of Parallelograms" Parallelogram PPT Download (Lesson 1):

"Determination of Parallelograms" Parallelogram PPT download (Lesson 1), 17 pages in total. Learning Objectives Explore and prove that a quadrilateral in which two sets of opposite sides are equal and one set of opposite sides are parallel and equal is a parallelogram; use the two sets of opposite sides to be equal and one set of parallel and equal sides..

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Update Time: 2024-11-21

This template belongs to Mathematics courseware Hebei Education Edition Eighth Grade Mathematics Volume 2 industry PPT template

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