"Determination of Parallelograms" PPT

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"Determination of Parallelograms" PPT

Part One: Properties of Parallelograms

Sides: Opposite sides are parallel and equal

Corollary: Parallel line segments sandwiched between two parallel lines are equal

Angles: opposite angles are equal, adjacent angles are complementary, four angles and 360°

Diagonals: bisect each other

Symmetry: Centrally symmetrical figure, the center of symmetry is the intersection of two diagonals

In the previous study, we analyzed the relevant characteristics of the sides, angles, and diagonals of a parallelogram and obtained its properties. On the contrary, what properties does a quadrilateral have that must be a parallelogram?

Tip: You can also think in terms of sides, angles, and diagonals

1. Utilization definition:

Two sets of opposite sides are parallel → parallelogram

Judgment of parallelograms PPT, part 2 content: problem exploration:

From the property theorem 1 of parallelograms, we know

Opposite sides of a parallelogram are equal, so is the opposite true?

It is known that in the quadrilateral ABCD, AB=CD and AD=BC.

Prove: Quadrilateral ABCD is a parallelogram.

hint:

Prove AB//CD, AD//BC

Judgment of parallelograms PPT, part 3: Judgment theorem of parallelograms

Parallelogram Determination Theorem 1:

If the two opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram

Briefly:

A quadrilateral with two equal sides is a parallelogram.

Parallelogram Determination Theorem 2:

If a set of opposite sides of a quadrilateral is parallel and equal, then the quadrilateral is a parallelogram

Briefly:

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

Judgment of Parallelograms PPT, Part 4: Selected Examples

Known: As shown in the figure, in □ABCD, E and F are the midpoints of sides AB and CD respectively.

Prove: Quadrilateral EBFD is a parallelogram.

Known: As shown in the picture, DC//EF//AB, DA//GH//CB, how many parallelograms are there in the picture?

Judgment of Parallelograms PPT, Part 5: Lesson Summary

Determination of parallelogram:

Two sets of opposite sides are parallel

Two sets of opposite sides are equal

A set of opposite sides are parallel and equal

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

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"Determination of Parallelograms" Parallelogram PPT Download (Lesson 3):

"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: 2024-10-05

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