What are the methods for determining rectangles, diamonds, and squares?

Square: A diamond with equal diagonal lines is a square.

Rectangles with diagonal lines perpendicular to each other are squares, and a square is a special type of rectangle.

The four sides are equal, and a quadrilateral with an angle of right angles is a square.

A set of rectangles with equal adjacent sides is a square.

A group of parallelograms with equal adjacent sides and one corner at right angles is a square.

A flat quadrilateral with all four sides equal and the diagonals bisected perpendicular to each other.

Rhombus: Rhomboid properties theorem 1

The four sides of the diamond are all equal.

Rhombic properties theorem 2

The diagonals of the diamond are perpendicular to each other, and each diagonal is bisected by a set of diagonals.

Rhomboid area = half of the diagonal product, i.e. s = (a b) 2 rhomboid decision theorem 1

A quadrilateral with all four sides equal is a diamond.

Rhomboidal Determination Theorem 2

A parallelogram with diagonal lines perpendicular to each other is a diamond.

must be equal; Not equal is not a diamond.

Definition: A diamond is a quadrilateral equal quadrilateral is a diamond;

Judgment: 1. A group of parallelograms with equal adjacent sides is a diamond.

2. A parallelogram with diagonal perpendicular to each other is a diamond.

3. A quadrilateral with equal sides is a diamond.

Rectangle: 1A parallelogram with equal diagonals.

2.There is a parallelogram with right angles.

A rectangle is a rectangle.

Rectangular nature. 1: The diagonal line of the rectangle.

Equal. 2: The four corners of the rectangle are all right angles.

Rectangle determination. 1: There is a parallelogram with a right angle at the angle.

is rectangular. 2: A parallelogram with equal diagonal lines is a rectangle.

3: A quadrilateral with 3 corners that are right angles is a rectangle.

Rhomboid-shaped nature. 1: All four sides of the diamond are equal.

2: The two diagonals of the diamond are perpendicular to each other, and each diagonal is bisected by a set of diagonals.

Rhombus determination. 1: There is a set of parallelograms with equal adjacent sides that are diamonds.

2. A parallelogram with diagonal perpendicular to each other is a diamond.

3: A quadrilateral with all four sides equal is a diamond.

Square nature.

1: All four corners of a square are right angles.

2: All four sides of the square are equal.

3: The squares are equal in diagonals and perpendicular to each other.

Square judgment.

1: A rectangle with equal adjacent sides is a square.

2: There is a diamond with a right angle that is a square.

3: A parallelogram that is bisected diagonally and perpendicular to each other is a square.

There are 5 ways to determine a square, namely: a diamond with equal diagonals is a square, a diamond with an angle at a right angle is a square, a rectangle with diagonal perpendicular to each other is a square, a group of rectangles with equal adjacent sides is a square, and a group of parallelograms with equal adjacent sides and a right angle is a square.

Square, is one of the special parallelograms. That is, a group of parallelograms with equal adjacent sides and one angle is at right angles is called a square, also known as a regular quadrilateral. Square, with all the characteristics of a rectangle and a rhombus.

Rectangle definition.

There is a parallelogram with a right angle called a rectangle. That is, a rectangle.

Property 1 The four corners of a rectangle are all right angles.

2 The diagonal lines of the rectangle are equal.

3 The sum of squares of the distance from any point in the plane of the rectangle to the ends of its two diagonals4 A rectangle is both axisymmetric and centrally symmetrical (the axis of symmetry is the line connecting the midpoints of any set of opposite sides).

5 pairs of sides are parallel and equal.

The 6 diagonals are bisected with each other.

7 The properties of parallelograms are possessed.

Rhombic properties:1It has all the properties of a parallelogram.

2.The four sides of the diamond are all equal to 3The diagonals of the diamond are perpendicular to each other, and each diagonal is bisected by a set of diagonals4

A rhombus is an axisymmetric figure. Square Nature: 1

The square has all the properties of a quadrilateral, parallelogram, rectangle, rhombus2Square property theorem:1

The four corners of the square are all right angles, and all four sides are equal.3 The theorem of square properties 2The two diagonals of the square are equal and bisected perpendicular to each other, and each diagonal is bisected by a set of diagonals4The square is an axisymmetric figure5

One diagonal line of the square divides the square into two congruent isosceles right triangles, and two diagonal lines divide the square into four small congruent isosceles right triangles. 6. One point on one diagonal of a square is equal to the distance between the ends of another diagonal.

The opposite sides are parallel and the opposite corners are equal ......The nature of parallelograms is their communal nature. Center-symmetrical, axis-symmetrical, diamond-shaped Rectangle = square.

The opposite sides are equal, the diagonals are equal, and the diagonals are bisected with each other, all of which are axisymmetric figures, and they are also all centrally symmetrical figures.

I.1Properties of rectangles:

The four corners of the rectangle are all straight horns.

The diagonal of the rectangle. Equal.

Rectangle discrimination method:

There is a quadrilateral with an angle that is right angled in parallel to this state. is rectangular.

A parallelogram with equal diagonal lines is a rectangle.

A quadrilateral with three corners that are right angles is a rectangle.

2.1. The properties of the rhombus are:

1) The relationship between the edges: parallel and equal.

2) The relationship between angles: the diagonal is equal, and the adjacent angles are complementary.

3), diagonal:

a. Quantitative relationship: divide each other equally.

b. Positional relationship: atrial parallel.

c. Other features: the four sides are equal.

2. Determination of diamond shape.

The methods are: 1) (Fixed.

Yi): A group of adjacent edges are equal.

2) (diagonal): bisected perpendicularly from each other.

3) (Side): The four sides are equal.

The nature of the rectangle: the inner angles of the four grandsons are all right angles; The diagonals are equal; It has all the properties of a parallelogram.

Decision: A parallelogram with equal diagonals is a rectangle; A quadrilateral with all four internal angles at right angles is rectangular.

The nature of the rhombus: the diagonals are bisected perpendicular to each other; All four sides are equal; It has all the properties of a parallelogram.

Determination of rhombus: a rolling source parallelogram with equal adjacent sides is a rhombus; A parallelogram with diagonals bisected perpendicular to each other is a diamond.

Side. Horn.

Diagonal parallelogram.

The opposite sides are parallel and equal.

The diagonal is equal. Diagonal alleys bisect each other's rectangles.

The opposite sides are parallel and equal.

All four corners are right angles.

The diagonals are bisected and equal to each other.

The opposite sides are parallel and the four sides are equal.

The diagonal is equal. The diagonals are bisected perpendicular to each other, and each diagonal is bisected by a set of corners.

Square silver liquid.

The opposite sides are parallel and the four sides are equal.

The four corners are all right-angled.

The diagonals are bisected perpendicular to each other and equal, with each diagonal bisecting a set of corners.

Two sets of quadrilaterals with equal diagonal diagonals are parallelograms, and quadrilaterals with diagonals bisecting each other are parallelograms; A parallelogram with equal diagonals is a rectangle (a quadrilateral with equal diagonals and bisected from each other is a rectangle); There is a group of parallelograms with equal adjacent sides that are diamonds.

The nature of the parallelogram1) The opposite sides of the parallelogram are parallel.

2) The opposite sides of the parallelogram are equal.

3) The parallelograms are equal in diagonals.

4) The adjacent angles of the parallelogram complement each other.

5) The two diagonals of the parallelogram are bisected from each other.

6) The parallelogram is a central symmetrical figure, and the symmetrical center is the intersection of two diagonals.

How to determine a parallelogram1) Two sets of quadrilaterals with opposite sides parallel to each other are parallelograms. (Definition) 2) Two sets of quadrilaterals with equal opposite sides are parallelograms.

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

Rectangle definition. There is a parallelogram with a right angle called a rectangle.

Rectangular nature. 1) The rectangle has all the properties of a parallelogram.

2: The four corners of the rectangle are all right angles.

3) The diagonal lines of the rectangle are equal and bisected from each other.

Rectangle determination method1) A parallelogram with a right angle is called a rectangle.

2) A quadrilateral with three angles that are right angles is a rectangular right triangle: the middle line on the hypotenuse of a right triangle is equal to half of the hypotenuse.

Diamond definitionThere is a set of parallel hunger quartets with equal adjacent sides called diamonds.

Rhomboid-shaped nature. 1) The rhombus has all the properties of a parallelogram.

2) The four sides of the rhombus are all equal.

3) The two diagonals of the diamond are perpendicular to each other, and each diagonal is bisected by a set of diagonals.

4) The rhombus is both a centrally symmetrical and an axisymmetric figure, and its axis of symmetry is the straight line where the diagonal line is located.

Diamond determination method1) A parallelogram with diagonal perpendicular to each other is a diamond.

2) A quadrilateral with all four sides equal is a diamond.

Squares are special diamond-shaped. A square must be a diamond, and a diamond is not necessarily a square. However, whether it is a square or a rhombic, their sides are equal.

Rhombus: In the same plane, there is a group of parallelograms with equal adjacent sides that are rhombus, quadrilaterals with equal sides are rhombus, the diagonals of the rhombus are bisected perpendicular to each other and bisect each group of diagonals, the rhombus is an axisymmetric figure, there are 2 symmetrical axes, that is, the straight line where the two diagonals are located, and the rhombus is a symmetrical figure in the center.

Square: A parallelogram with equal adjacent sides and one corner at a right angle is called a square. There is a group of rectangles with equal adjacent sides called squares, and there is a diamond with an angle of 90° called a square. The square is a special form of a rectangle and a special form of a diamond.

1. The square type is that the four sides are equal, the four corners are right angles, and the diagonal lines are opposite.

2. Although the four sides of the diamond shape are equal, the four corners are not necessarily equal, and the diagonals are perpendicular to each other but not necessarily equal.

1. A group of parallelograms with equal adjacent sides is a rhombus;

2. A parallelogram with diagonal perpendicular to each other is a diamond.

3. A quadrilateral with equal four sides is a diamond;

4. A quadrilateral with diagonals bisected perpendicular to each other;

5. Two diagonal lines divide each group of diagonal quadrilaterals separately;

6. There is a parallelogram with a diagonal bisecting an inner angle.

As long as the four sides are of equal length, they are all diamond-shaped So the square is also a kind of diamond square is the length of the four sides, and the four corners are equal to < 90 degrees The square is not a diamond, the diamond is a square 2009-03-07 20:48:43 Supplement:

sorry type wrong correct one: As long as the four sides are of equal length, they are all diamonds and squares So the square is not a type of diamond Square is the length of the four sides, and the four corners are equal to 90 degrees But the diamond is the length of the four sides, and the four corners are all < 90 degrees The square is not a diamond, and the diamond is not a square.

It is found that Guan Zhaozheng is imitating the definition of a rhombus - a quadrilateral with four sides of equal length before the Qing Dynasty; is a type of parallelogram; The diagonal is equal. The diagonals are perpendicular and bisected from each other; Area = diagonal length product divided by two; [square] [belongs] [diamond-shaped] [exception].

As long as the four sides are of equal length, they are all diamond-shaped, so the square is also a kind of diamond-shaped, and the square is the length of the four sides, and the four corners are equal to 90 degrees, the square is a diamond, but the diamond is not necessarily a square.

Lozenge. Has all parallelogram properties, including diagonal equality.

The opposite sides are equal. The opposite sides are parallel and equal.

The diagonal lines are bisected with each other. The rhombic middle includes: The four families have equal fiber edges.

The diagonals are perpendicular to each other (the intersection is 90 degrees) and diamond-shaped.

Rectangles are special quadrilaterals, and squares are all systematic.

Because the square has parallelograms.

Diamonds and rectangles are characteristic.

Reference: Yourself.