"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 4

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"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware 4

Warm up before class

1. The four interior angles of the rectangle are ______.

2. The diagonals of the rectangle are ______ and __________.

3. A rectangle is a _______ symmetrical figure.

4. In a right triangle, the right side opposite to the ______ angle is equal to the _______ of the hypotenuse.

5. In a right triangle, ______ on the hypotenuse is equal to ______ on the hypotenuse.

Are the following statements about rectangles correct?

(1) A quadrilateral with one right angle is a rectangle; ( )

(2) A quadrilateral with four equal angles is a rectangle; ( )

(3) A quadrilateral with four right angles is a rectangle. ( )

(4) A quadrilateral with equal diagonals is a rectangle; ( )

(5) A quadrilateral whose diagonals bisect each other and are equal is a rectangle ( )

(6) A quadrilateral with two sets of opposite sides parallel and equal diagonals is a rectangle. ( )

expand:

(1) Is a quadrilateral with equal diagonals a rectangle?

(2) What conditions need to be added to make a quadrilateral with equal diagonals a rectangle?

induction:

A quadrilateral with equal diagonals that bisect each other is a rectangle

∵ AC=BD and OA=OC OB=OD

∴ Quadrilateral ABCD is a rectangle

Now you can help your carpenter friends to detect whether the window frame you made is rectangular. What data can you measure? What are the several solutions and what are the basis?

Solution: Measure the lengths of two sets of opposite sides and the measure of an interior angle. If the lengths of the two sets of opposite sides are equal and the interior angle is a right angle, then the window frame meets the specifications.

Solution: Measure the three interior angles. If the three interior angles are all right angles, the window frame meets the specifications.

Solution: Measure the lengths of the four sides and two diagonals of the window frame respectively. If the lengths of the two opposite sides of the window frame and the lengths of the two diagonals are equal, then the window frame meets the specifications.

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Update Time: 2024-09-09

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