Definition of rectangle
In geometry, a rectangle is defined as a quadrilateral with four equal internal angles, that is, all internal angles are right angles.
From this definition, it can be concluded that two opposite sides of a rectangle are equal in length, that is, a rectangle is a parallelogram. A square is a special case of a rectangle, and its four sides are all equal in length. At the same time, a square is both a rectangle and a diamond. A rectangle that is not a square is usually called a rectangle.
Basic introduction of rectangle
Rectangle * * Rectangle * * is a plane figure. The four corners of a rectangle are right angles, the diagonals of the rectangle are equal, and the sum of squares of the distances from any point on the plane of the rectangle to the endpoints of its two diagonals is equal.
decision
1. A parallelogram with right angles is a rectangle.
2. Parallelograms with equal diagonals are rectangles.
A quadrilateral with three right angles is a rectangle.
4. Quadrilaterals with equal diagonals and bisecting each other are rectangles.
Description: Rectangles and squares are rectangles. The definition of parallelogram still applies to rectangle.
cartography
A rectangle must have one set of opposite sides parallel to the X axis and another set of opposite sides parallel to the Y axis. Geometric rectangles that do not meet this condition are regarded as general quadrilaterals in computer graphics. "Only the rectangle is mentioned in advanced mathematics, so the length and width of the rectangle are not mentioned.
Detailed explanation of rectangle
computing formula
Area: S=ab*** Note: A is the length and B is the width * * *
Circumference: C=2***a+b***=2a+2b*** Note: A is the length and B is the width * * *
circumcircle
The radius of the circumscribed circle of the rectangle R= half of the diagonal of the rectangle
nature
1. The four internal angles of a rectangle are right angles;
2. The diagonals of the rectangle are equal and equally divided;
3. The sum of squares of the distances from any point on the rectangular plane to its two diagonal endpoints is equal;
4. Rectangle is not only an axisymmetric figure, but also a central symmetric figure. * * * Symmetry axis is a straight line connecting the midpoints of any group of opposite sides, and it has at least two symmetry axes.
5. A rectangle has all the characteristics of a parallelogram.
6. The quadrilateral obtained by connecting the midpoints of each side of the rectangle in turn is a diamond.
Golden rectangle
A rectangle with an aspect ratio of * * √ 5- 1 * */2 * * is called a golden rectangle.
The golden rectangle gives us a harmonious and symmetrical aesthetic feeling. In order to get the best visual effect, many famous buildings around the world have adopted the design of golden rectangle. Such as the Parthenon in Greece.
Judgement application of rectangle
Example 1: It is known that the diagonal AC and BD of ABCD intersect at point O, △AOB is an equilateral triangle and AB= 4 cm. Find the area of this parallelogram.
Analysis: Firstly, according to the fact that △AOB is an equilateral triangle and the diagonal of parallelogram is bisected, it is determined that ABCD is a rectangle, and then the side length is calculated by Pythagorean theorem, so the area is
Example 2: It is known that in ABCD, m is the midpoint of BC, ∠MAD=∠MDA. Prove that the quadrilateral ABCD is a rectangle.
Analysis: According to the definition, it is proved that an angle is a right angle, which can be realized by △ABM≌DCM***SSS***.
Example: 3: It is known that the four bisectors of ABCD intersect at points E, F, G and H, and it is proved that EG=FH.
Analysis: EG and FH to be proved are diagonal lines of quadrilateral EFGH, so only need to prove that quadrilateral EFGH is a rectangle, and the topic can be decomposed into basic figures: therefore, you can choose "quadrilateral with three right angles is a rectangle" to prove it.
It depends. Very complicated and tedious variants can be omitted, regular and commonly used formulas must be writte