"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 7

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"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 7

Situation one

As shown in the figure, on a parallelogram movable frame, two rubber bands are placed on two opposite vertices respectively. When a pair of non-adjacent vertices is pulled, what will happen to the shape of the parallelogram?

Question (1): How will the length of the two diagonals change as ∠a changes?

Question (2): What are the characteristics of a parallelogram when the lengths of its two diagonals are equal? What guess can you get from this?

Scenario 2

Student Li Fang drew a quadrilateral in four steps. Her drawing method was "side-right angle, side-right angle, side-right angle, side." She said this is a rectangle. Is her judgment correct? Why?

Conjecture: A quadrilateral with three right angles is a rectangle.

Is a quadrilateral with three right angles a rectangle?

Known: As shown in the figure, in the quadrilateral ABCD, ∠A=∠B=∠C=90°.

Prove: Quadrilateral ABCD is a rectangle.

Prove: ∵∠A=∠B=∠C=90°,

∴∠A+∠B=180°,∠B+∠C=180°.

∴AD∥BC,AB∥CD.

∴ Quadrilateral ABCD is a parallelogram.

∴ Quadrilateral ABCD is a rectangle.

Discuss:

1. How can you tell whether a quadrilateral is a parallelogram if there is only a longer rope?

2. If there is only a longer rope, how do you determine whether a quadrilateral is a rhombus?

3. How can you tell if a quadrilateral is a rectangle if there is only a longer rope?

How to determine a rectangle:

A parallelogram with one right angle is a rectangle.

A parallelogram with equal diagonals is a rectangle.

A quadrilateral with three right angles is a rectangle.

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Update Time: 2024-10-02

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