"Parallelograms and Their Properties" PPT Courseware 6

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"Parallelograms and Their Properties" PPT Courseware 6

1. The concept of parallelogram:

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

2. Characteristics: a. It is a quadrilateral; b. There are two sets of opposite sides that are parallel.

3. Symbol: "□" For example, parallelogram ABCD is recorded as: □ABCD; read as: parallelogram ABCD

4. Relevant names:

(1) Opposite side, (2) Adjacent side;

(3) Opposite angles, (4) Adjacent angles;

(5) High.

Typical examples (1)

1. As shown in the figure: □ABCD, EF∥AB,

①Then there are __parallelograms in the picture;

②If GH∥AD, EF and GH intersect at point O, then there are __parallelograms in the figure.

Discussion 

1. What are the properties of the sides of a parallelogram? Tell us your reasons.

2. What are the properties of the angles of a parallelogram? Tell us your reasons.

Properties of parallelograms:

1. Opposite sides of a parallelogram are parallel and equal

2. Opposite angles of a parallelogram are equal.

Properties of parallelograms

Theorem 1: Opposite sides of a parallelogram are equal.

Known: As shown in the figure, quadrilateral ABCD is a parallelogram.

Prove: AB=CD, BC=DA.

Analysis: To prove that AB=CD and BC=DA can be proved by converting the corresponding sides of congruent triangles, auxiliary lines can be drawn to achieve the purpose.

Proof: Connect AC.

∵ Quadrilateral ABCD is a parallelogram,

∴AB∥CD,BC∥DA.

∴∠1=∠2, ∠3=∠4.

In △ABC and △CDA, ∠1=∠2, AC=CA, ∠3=∠4

∴△ABC≌△CDA(ASA).

∴AB=CD,BC=DA.

Property application

Typical examples (2)

A: Basic knowledge:

If ∠A=130°, then ∠B=______, ∠C=______, ∠D=______

B: Variation training:

1. If ∠A+ ∠C= 200°, then ∠A=______, ∠B=______

2. If ∠A:∠B= 5:4, then ∠C=______, ∠D=______

Variation exercises:

As shown in the figure: In □ABCD, ∠A+∠C=200°

Then: ∠A=______, ∠B=______.

Solution: ∵ Quadrilateral ABCD is a parallelogram

And ∠A+∠C=200°

∴∠A=∠C=100 ° (opposite angles of a parallelogram are equal)

Also ∵AD∥BC (opposite sides of a parallelogram are parallel)

∴∠B= 180 °－∠A= 180º－ 100°=80°

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"Parallelograms and Their Properties" PPT courseware 5:

"Parallelograms and Their Properties" PPT Courseware 5 Knowledge Review Definition A quadrilateral with two sets of opposite sides that are parallel is a parallelogram. Properties: Opposite sides of a parallelogram are parallel and equal; Opposite angles of a parallelogram are equal; Adjacent angles are complementary. Caught between two parallel lines...

"Parallelograms and Their Properties" PPT courseware 4:

"Parallelogram and Its Properties" PPT Courseware 4 Review: 1. What is a parallelogram? How to express? 2. What are the properties theorems of parallelograms? 3. How to express its property theorem in geometric language? Experiments and Inquiries Please read Chapter 6 of the textbook carefully.

"Parallelograms and Their Properties" PPT courseware 3:

"Parallelograms and Their Properties" PPT courseware 3 Parallelogram concept: A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram. Opposite sides: AB and CD, AD and BC Opposite angles: DAB and BCD, ABC and CDA Diagonals: AC, BD Mathematical symbols of parallelograms:..

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Update Time: 2024-07-05

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