Correct rectangle. Rectangle

Rectangle … Spelling Dictionary

Parallelogram, quadrilateral, square Dictionary of Russian synonyms. rectangle n., number of synonyms: 4 square (9) ... Synonym dictionary

A term used in the technical analysis of financial market conditions to refer to price movements that fit into a rectangle on a chart. Raizberg B.A., Lozovsky L.Sh., Starodubtseva E.B. Modern economic dictionary. 2nd ed., corrected ... Economic dictionary

Glossary of business terms

RECTANGLE, parallelogram, all angles of which are right ... Modern Encyclopedia

A quadrilateral with all right angles... Big Encyclopedic Dictionary

RECTANGLE, four-sided geometric figure(quadrilateral) whose interior angles are right and opposite sides are pairwise parallel and equal. it a special case PARALLELOGRAM ... Scientific and technical encyclopedic dictionary

RECTANGLE, rectangle, male. (geom.). A quadrilateral in which all angles are right. Dictionary Ushakov. D.N. Ushakov. 1935 1940 ... Explanatory Dictionary of Ushakov

RECTANGLE, a, husband. 1. A quadrilateral with all right angles. 2. The name of the officer's insignia of this form on the buttonholes in the Red Army (from 1924 to 1943). Explanatory dictionary of Ozhegov. S.I. Ozhegov, N.Yu. Shvedova. 1949 1992 ... Explanatory dictionary of Ozhegov

A type of price movement chart in the form of a triangle, used in the technical analysis of financial markets. Dictionary of business terms. Akademik.ru. 2001 ... Glossary of business terms

Books

• Rectangle (+ stickers), Valeria Vilyunova. This sticker book is designed for the youngest readers. At 2 years old, the child performs with pleasure exciting tasks sticking the stickers in the right place. This activity is not only…
• Rectangle, Vilyunova V.A. The book "Rectangle" is intended for the smallest readers. With its help, your baby will get acquainted with geometric shapes - a rectangle and a trapezoid, learn to distinguish and name ...

Geography, biology, chemistry, algebra, geometry... Schoolchildren have to deal with a lot of information from a wide variety of sciences. However, there are areas of knowledge in which it is quite easy to understand, having familiarized yourself with their basic laws. Geometry is one of them. To know all the subtleties of this science, you must definitely get acquainted with its basics, axioms. After all, without the foundations in geometry, nowhere.

Definition of a rectangle

A rectangle is a geometric figure with four right angles. The definition is quite simple, but you should not think that the student will not have problems studying such a topic, because there are a number of features here. The dimensions of a rectangle depend on the length of its sides, which are most often denoted by the Latin letters a and b.

Rectangle properties

• the sides lying opposite each other are equal and parallel;
• the diagonals of the figure are equal;
• the intersection point of the diagonals bisects them;
• a rectangle can be divided into two equal

Rectangle Features

There are only three features that a rectangle has. Here they are:

• a parallelogram with equal diagonals is a rectangle;
• a parallelogram with one right angle is a rectangle;
• a quadrilateral with three right angles is a rectangle.

A little more interesting

So, what a rectangle is is now clear, but what role it plays in geometric problems and in practical measurements has yet to be figured out. So, first of all, it must be said that this is the most convenient geometric figure, with which you can divide the area into sections both in open areas and indoors.

What is a rectangle? As you know, it is a quadrilateral. There are many varieties of the latter, among which one can name a trapezoid (only two sides are equal), a parallelogram (opposite sides are parallel), a square (all angles and sides are the same), a rhombus (a parallelogram with equal sides) and others. A special case of a rectangle is a square, in which all angles are right, and the sides are equal.

It is impossible to talk about what a rectangle is without mentioning how to determine its dimensions. This area is considered to be the product of its width and length, and the perimeter, like that of any figure, is equal to the sum of the lengths of all sides. In this case, it is also equal to twice the sum of the length and width, since the opposite sides of the rectangle are equal. Now you know what a rectangle is and what to do with it, solving problems and comprehending the secrets of such a mysterious and mysterious science as geometry.

Rectangle is a quadrilateral in which every corner is a right angle.

Proof

The property is explained by the action of feature 3 of the parallelogram (i.e. \angle A = \angle C , \angle B = \angle D )

2. Opposite sides are equal.

AB = CD,\enspace BC = AD

3. Opposite sides are parallel.

AB \parallel CD,\enspace BC \parallel AD

4. Adjacent sides are perpendicular to each other.

AB \perp BC,\enspace BC \perp CD,\enspace CD \perp AD,\enspace AD ​​\perp AB

5. The diagonals of the rectangle are equal.

AC=BD

Proof

According to property 1 the rectangle is a parallelogram, which means AB = CD.

Therefore, \triangle ABD = \triangle DCA along two legs (AB = CD and AD - joint).

If both figures - ABC and DCA are identical, then their hypotenuses BD and AC are also identical.

So AC = BD .

Only a rectangle of all figures (only from parallelograms!) Has equal diagonals.

Let's prove this too.

ABCD is a parallelogram \Rightarrow AB = CD , AC = BD by condition. \Rightarrow \triangle ABD = \triangle DCA already on three sides.

It turns out that \angle A = \angle D (like the corners of a parallelogram). And \angle A = \angle C , \angle B = \angle D .

We deduce that \angle A = \angle B = \angle C = \angle D. They are all 90^(\circ) . The total is 360^(\circ) .

Proven!

6. The square of the diagonal is equal to the sum of the squares of its two adjacent sides.

This property is valid by virtue of the Pythagorean theorem.

AC^2=AD^2+CD^2

7. The diagonal divides the rectangle into two identical right triangles.

\triangle ABC = \triangle ACD, \enspace \triangle ABD = \triangle BCD

8. The intersection point of the diagonals bisects them.

AO=BO=CO=DO

9. The point of intersection of the diagonals is the center of the rectangle and the circumscribed circle.

10. The sum of all angles is 360 degrees.

\angle ABC + \angle BCD + \angle CDA + \angle DAB = 360^(\circ)

11. All corners of the rectangle are right.

\angle ABC = \angle BCD = \angle CDA = \angle DAB = 90^(\circ)

12. The diameter of the circumscribed circle around the rectangle is equal to the diagonal of the rectangle.

13. A circle can always be described around a rectangle.

This property is valid due to the fact that the sum of the opposite corners of a rectangle is 180^(\circ)

\angle ABC = \angle CDA = 180^(\circ),\enspace \angle BCD = \angle DAB = 180^(\circ)

14. A rectangle can contain an inscribed circle and only one if it has the same side lengths (it is a square).

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A rectangle is a parallelogram in which all angles are right angles (equal to 90 degrees). The area of ​​a rectangle is equal to the product of its adjacent sides. The diagonals of a rectangle are equal. The second formula for finding the area of ​​a rectangle comes from the formula for the area of ​​a quadrilateral in terms of diagonals.

Rectangle is a quadrilateral in which every corner is a right angle.

The square is special case rectangle.

A rectangle has two pairs of equal sides. The length of the longest pair of sides is called rectangle length, and the length of the shortest - rectangle width.

Rectangle properties

1. A rectangle is a parallelogram.

The property is explained by the action of feature 3 of the parallelogram (that is, \(\angle A = \angle C \) , \(\angle B = \angle D \) )

2. Opposite sides are equal.

\(AB = CD,\enspace BC = AD \)

3. Opposite sides are parallel.

\(AB \parallel CD,\enspace BC \parallel AD \)

4. Adjacent sides are perpendicular to each other.

\(AB \perp BC,\enspace BC \perp CD,\enspace CD \perp AD,\enspace AD ​​\perp AB \)

5. The diagonals of the rectangle are equal.

\(AC = BD\)

According to property 1 the rectangle is a parallelogram, which means \(AB = CD \) .

Consequently, \(\triangle ABD = \triangle DCA \) on two legs (\(AB = CD \) and \(AD \) - joint).

If both figures - \(ABC \) and \(DCA \) are identical, then their hypotenuses \(BD \) and \(AC \) are also identical.

So \(AC = BD \) .

Only a rectangle of all figures (only from parallelograms!) Has equal diagonals.

Let's prove this too.

\(\Rightarrow AB = CD \) , \(AC = BD \) by condition. \(\Rightarrow \triangle ABD = \triangle DCA \) already on three sides.

It turns out that \(\angle A = \angle D \) (like the corners of a parallelogram). And \(\angle A = \angle C \) , \(\angle B = \angle D \) .

We deduce that \(\angle A = \angle B = \angle C = \angle D \). All of them by \(90^(\circ) \) . The sum is \(360^(\circ) \) .

7. The diagonal divides the rectangle into two identical right triangles.

\(\triangle ABC = \triangle ACD, \enspace \triangle ABD = \triangle BCD \)

8. The intersection point of the diagonals bisects them.

\(AO = BO = CO = DO \)

9. The intersection point of the diagonals is the center of the rectangle and the circumscribed circle.