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

Description

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

Properties of parallelograms:

Opposite sides of a parallelogram are parallel;

Opposite sides of a parallelogram are equal;

The diagonals of a parallelogram bisect each other;

Opposite angles of a parallelogram are equal;

The adjacent angles of a parallelogram are complementary;

Rectangle definition

Definition: A parallelogram with one right angle is called a rectangle

Our lives are full of geometric shapes like rectangles. The blackboards, doors and windows in the classroom, the tabletops of desks, envelopes and postcards are all in rectangular shapes. Do you know what a rectangle is? Do you understand the properties of this geometric figure?

Activity 1

On a parallelogram movable frame, use two rubber bands to put on two opposite vertices respectively, and pull a pair of non-adjacent vertices to change the shape of the parallelogram.

(1) As ∠a changes, how do the lengths of the two diagonals change?

As ∠a changes, one diagonal becomes longer and the other becomes shorter.

(2) When ∠a becomes a right angle, the parallelogram forms a rectangle. What are its other internal angles?

All become right angles

(3) When ∠a is a right angle, the parallelogram becomes a rectangle. What is the relationship between the lengths of the two diagonals?

Two diagonals are equal

Properties of rectangle

The two diagonals of a rectangle are equal.

It is known that AC and BD are the two diagonals of the rectangle ABCD.

Explanation:AC=BD.

Analysis: According to the properties of rectangles, it can be converted into congruent triangles (SAS) to prove.

Discuss:

Assume that the diagonals AC and BD of the rectangle intersect at point E. Then, what kind of special line segment is BE in Rt△ABC?

BE is the midline on the hypotenuse AC in Rt△ABC.

What is its size relationship with AC? Why?

BE is equal to half of AC.

From this we can deduce:

The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse

practice

Quadrilateral ABCD is a rectangle

1. If it is known that AB=8�, AD=6�,

Then AC=______� OB=______�

2. If ∠CAB=40° is known, then ∠OCB=

∠OBA=______ ∠AOB=______ ∠AOD=______

3. If it is known that AC=10� and BC=6�, then the perimeter of the rectangle=______�

Area of ​​rectangle=______ �²

4 If it is known that ∠DOC=120°, AD=6�, then AC=______�

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Update Time: 2024-10-01

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