"Determination of Parallelograms" PPT courseware

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"Determination of Parallelograms" PPT courseware

Review the past and learn the new

Opposite sides of a parallelogram are parallel and equal

∵ Quadrilateral ABCD is a parallelogram ∴ AB∥=CD, AD∥=BC

Opposite angles of a parallelogram are equal and adjacent angles are complementary

∵ Quadrilateral ABCD is a parallel polygon

∴ ∠ A=∠ C, ∠ D=∠ B

∠ A+∠ B=180° , ∠ A+∠ D=180° …

The diagonals of a parallelogram bisect each other

∵ Quadrilateral ABCD is a parallel polygon

∴OA=OC,OB=OD

1. Think about it

real life challenges

Yesterday, Li Ming, a first-year junior high school student, accidentally broke a parallelogram-shaped experimental glass piece in the laboratory while doing experiments in the biology laboratory. Only the part shown in the picture was left. He wanted to go home and cut it tomorrow, Saturday. One piece was paid to the school. It was not safe to take the remaining part of the glass to the glass shop, so he wanted to draw the original parallelogram on paper again? Then he could just bring the drawing, but how to draw the original parallelogram? Woolen cloth? (A, B, and C are three vertices, that is, find the fourth vertex D)

2. One certificate

A quadrilateral with two equal sides is a parallelogram.

Symbolic language:

∵AB=CD,AD=BC

∴ Quadrilateral ABCD is a parallelogram

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

Prove: Quadrilateral ABCD is a parallelogram

Proof: Link AC

In △ABC and △CDA

AB=CD (known)

AD=CB (known)

AC=CA (common edge)

∴△ABC≌△CDA (SSS)

∴∠1=∠2, ∠3=∠4 (corresponding angles of congruent triangles are equal)

∴ AB∥CD, AD∥BC (the internal offset angles are equal and the two straight lines are parallel)

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

3. Guess

Please write the converse of the following property theorem and judge whether it is correct or not? Give it a try!

(3) A set of quadrilaterals whose opposite sides are parallel and equal is a parallelogram.

Symbolic language: ∵AB∥�CD ∴ Quadrilateral ABCD is a parallelogram

(4) The two opposite angles of a parallelogram are equal

Converse Proposition: A quadrilateral with two equal opposite angles is a parallelogram.

Symbolic language: ∵∠A=∠C,∠B=∠D

∴ Quadrilateral ABCD is a parallelogram

(5) The diagonals of a parallelogram bisect each other

Converse proposition: A quadrilateral whose diagonals bisect each other is a parallelogram.

Symbolic language:

∵OA=OC,OB=OD

∴ Quadrilateral ABCD 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 (definition)

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

6. Let’s talk about it:

1. In this lesson you have learned several methods of determining parallelograms.

2. The ideas for solving problems learned in this lesson are:

(1) Solving a mathematical problem often requires "hands-on practice"-----"

Conjecture"-----"Verify the conjecture (proof)"-----"Draw a conclusion"

(2) Problems encountered with parallelograms are often solved by converting them into triangles.

1. As shown in the figure, EF=MN is intercepted on a set of opposite sides AD and BC of parallelogram ABCD, and EM and FN are connected. What is the relationship between EM and FN? Why?

2. As shown in the figure, E and F are two points on the diagonal AC of the quadrilateral ABCD, AF=CE, DF=BE, DF∥BE.

Prove: Quadrilateral ABCD is a parallelogram.

3. As shown in the figure, O is the midpoint of the diagonal AC of □ABCD.

The straight line EF passing through point O intersects AB and CD at two points E and F respectively.

Prove: Quadrilateral AECF is a parallelogram.

4. As shown in the figure, AC is a diagonal of ABCD.

BM⊥AC, ND⊥AC, and the vertical feet are M and N respectively.

Prove: Quadrilateral BMDN is a parallelogram.

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"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:

"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..

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Update Time: 2024-08-02

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

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