"Properties and Judgment of Rhombus" Special Parallelogram PPT Courseware 2

Description

"Properties and Judgment of Rhombus" Special Parallelogram PPT Courseware 2

Exploration 1

Use two thin wooden strips, one long and one short, and fix a small nail at their midpoint to make a rotatable cross. Put a rubber band around it to make a quadrilateral. Rotate the wooden strips. What is this quadrilateral? When does it become a rhombus?

Conjecture: A parallelogram with mutually perpendicular diagonals is a rhombus.

Exploration 2

First draw two line segments AB and AD of equal length, and then draw arcs with B and D as the center and AB as the radius. Get the intersection point C of the two arcs. Connect BC and CD to get a quadrilateral. Guess, this What is a quadrilateral? tell me your reasons

Guess: A quadrilateral with four equal sides is a rhombus.

Proposition: A quadrilateral with four equal sides is a rhombus.

Known: In the quadrilateral ABCD, AB=BC=CD=DA.

Prove: Quadrilateral ABCD is a rhombus

Prove: ∵AB=CD,AD=BC

∴ Quadrilateral ABCD is a parallelogram

And ∵AB=AD,

∴Quadrilateral ABCD is a rhombus

How to use origami and cutting methods to quickly and accurately cut out a diamond-shaped piece of paper?

Some students did this: fold a rectangular piece of paper in half, then fold it in half again, then cut it along the dotted line in the picture and open it. Do you know the reason?

Commonly used determination methods for diamond shapes:

(1) There is a set of parallelograms with equal adjacent sides called a rhombus.

(2) A parallelogram with mutually perpendicular diagonals is a rhombus

(3) A quadrilateral with four equal sides is a rhombus.

Try this exercise:

1. The teacher said that the following three shapes are all rhombuses. Do you believe it?

A set of parallelograms with equal adjacent sides is called a rhombus

A parallelogram with perpendicular diagonals is a rhombus

A quadrilateral with four equal sides is a rhombus.

2. Determine whether the following statements are correct? Why?

(1) A quadrilateral with perpendicular diagonals is a rhombus; ( )

(2) A quadrilateral whose diagonals bisect each other perpendicularly is a rhombus; ( )

(3) A quadrilateral whose diagonals are perpendicular to each other and has a set of equal adjacent sides is a rhombus; ( )

(4) A quadrilateral with two adjacent sides equal to one diagonal bisecting a set of diagonals is a rhombus. ( )

3. The diagonals AC and BD of □ABCD intersect at point O,

(1) If AB=AD, then □ABCD is ____ shape;

(2) If ∠BAO=∠DAO, then □ABCD is ____ shape.

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Update Time: 2024-09-09

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