Parallelogram properties:

1, and the opposite sides of the parallelogram are equal.

2. The diagonals of parallelograms are equal.

3. The diagonal of parallelogram is equally divided.

Parallelogram judgment:

1, two sets of quadrilaterals with equal opposite sides are parallelograms.

2. Quadrilaterals whose diagonals bisect each other are parallelograms.

3. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

4. Two groups of diagonally equal quadrilaterals are parallelograms.

5. Two groups of parallelograms with parallel opposite sides are parallelograms.

Rectangular properties:

(1) has all the properties of a parallelogram.

(2) Uniqueness: All four corners are right angles and diagonal lines are equal.

Rectangular decision:

1, a parallelogram with a right angle is called a rectangle.

A quadrilateral with three right angles is a rectangle.

3. A parallelogram with equal diagonals is a rectangle.

Diamond properties:

1 has all the properties of a parallelogram.

All four sides of the diamond are equal.

3. The diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals.

4. Diamond area = bottom × height = half of diagonal product.

Diamond decision:

1, a set of parallelograms with equal adjacent sides is called a diamond.

2. A quadrilateral with four equilateral sides is a diamond.

3. Parallelograms with diagonal lines perpendicular to each other are rhombic.

Properties of Square: Square has all the properties of quadrilateral, parallelogram, rectangle and diamond.

How to judge the square:

1, it is proved to be a rectangle first, and then it is proved that a group of adjacent sides are equal or diagonal is vertical.

2. First prove that it is a diamond, and then prove that it has a right angle or diagonal equal.

Introduction to Mathematics:

Mathematics: English: Mathematics, which originated from the ancient Greek μ θ η μ α (má th ē ma); Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information. Mathematics is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence.

In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics. Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.