Diagonal parallelepipeda for the backward sum of the squares of the three. The value of the parallelepiped. Basic power and formulas. Parallelepiped i yogo vidi
At the end of the day, you can learn the theme "Straightforward parallelepiped". On the ear of the lesson, we can repeat it, but also a decent and straight parallel line, guessed by the power of the other sides and diagonals of the parallel line. It is clear that it is also straight-forward parallelepiped, and the main power is discussed.
Topic: Perpendicularity of straight lines and areas
Lesson: Rectangular parallelepiped
The top, folded from two parallelograms ABCD and A 1 B 1 C 1 D 1 and some parallelograms ABB 1 A 1, BCC 1 B 1, CDD 1 C 1, DAA 1 D 1, be called parallelepiped(Fig. 1).
Small. 1 Parallelepiped
Tobto: at most two parallelograms ABCD and A 1 B 1 C 1 D 1 (aside), the stench lie in parallel areas so that the ribs AA 1, BB 1, DD 1, CC 1 are parallel. This rank, folded from parallelograms on the surface, is called parallelepiped.
In such a rank, the surface of the parallelepiped is the sum of all parallelograms, including the number of parallelepipeds.
1. The prototypes are parallel and parallel.
(Figuri rivni, so you can have one overlap)
for example:
ABCD = A 1 B 1 C 1 D 1 (equal parallelograms for values),
АА 1 В 1 В = DD 1 С 1 С (so yak АА 1 В 1 В і DD 1 С 1 С - opposite sides of parallelepiped),
AA 1 D 1 D = BB 1 C 1 C (so yak AA 1 D 1 D і BB 1 C 1 C - opposite sides of the parallelepiped).
2. Diagonals of parallelepipeds are interlaced in one point and spread over a single point of navpil.
Diagonal parallelepipeda AC 1, B 1 D, A 1 C, D 1 B are interlaced in one point O, and the skin diagonal extends over a whole point of navpil (Fig. 2).
Small. 2 Diagonals of parallelepipeds are overturned and overlapped by a point.
3. Є three quadruples of parallel and parallel ribs of parallelepiped: 1 - AB, A 1 B 1, D 1 C 1, DC, 2 - AD, A 1 D 1, B 1 C 1, BC, 3 - AA 1, BB 1, CC 1, DD 1.
Viznachennya. Parallelepiped is called straight, as well as the ribs perpendicular to the sides.
Do not bichne rib AA 1 perpendicular to the base (Fig. 3). Tse means that the straight line AA 1 is perpendicular to the straight lines AD and AB, which lie in the area of \ u200b \ u200bpart. And, it means, in bichnyh facets lie rectangulars. And in pіdstavah lie pretty parallelograms. Apparently, ∠BAD = φ, qut φ can be-yak.
Small. 3 Straight parallelepiped
Otzhe, straight parallelepiped - tse parallelepiped, in which bichni ribs perpendicular to the paralelepiped.
Viznachennya. Parallelepiped is called straight-headed, every single rib is perpendicular to the base. Pidstavi є rectangular.
Parallelepiped ABCDE 1 B 1 C 1 D 1 - rectangular (Fig. 4), where:
1. AA 1 ⊥ ABCD (sometimes the edge is perpendicular to the area of the front, so that it is parallel to the straight line).
2. ∠BAD = 90 °, ie. In the basis there is a rectangle.
Small. 4 Rectangular parallelepiped
The upright parallelepiped has all the power of the pre-parallelepiped. Alle additional power, as a result of the designation of a rectangular parallelepiped.
Otzhe, rectangular parallelepiped- tse parallelepiped, at which bichni ribs are perpendicular to the base. Pidstava rectangular parallelepipeda - rectangular.
1. The rectangular parallelepiped has all the number of faces of the rectangular.
ABCD і А 1 В 1 С 1 D 1 - rectangulars for design.
2. Bichni ribs perpendicular to the base... This means that all the biches of the rectangular parallelepiped are rectangulars.
3. All dihedral kuti of a rectangular parallelepiped are straight.
It is clear, for example, a dihedral cut of a rectangular parallelepiped with an edge AB, i.e., a dihedral cut between areas ABB 1 and ABC.
AB is an edge, point A 1 lies in one area - in area ABB 1, and point D in the other - in area A 1 B 1 C 1 D 1. The appearance of the two-sided cut can be significant by the following rank: ∠A 1 ABD.
Go to point A on the edge AB. AA 1 - perpendicular to edge AB in area ABB-1, AD perpendicular to edge AB in area ABC. This means that ∠А 1 АD is the line cut of the given dihedral cut. ∠А 1 АD = 90 °, which means, a two-sided kut at the edges AB doors 90 °.
∠ (ABB 1, ABC) = ∠ (AB) = ∠A 1 ABD = ∠A 1 AD = 90 °.
Similarly, it should be done, whether it be two-sided kuti of a rectangular parallelepiped straight.
Square of diagonal rectangular parallelepiped for transporting squares three times.
Note. Dovzhini three ribs, which go from one vertex of a rectangular parallelepiped, є vimirs of a rectangular parallelepiped. Їх inodі name the amount, width, height.
Given: ABCD 1 B 1 C 1 D 1 - rectangular parallelepiped (Fig. 5).
Bring :.
Small. 5 Rectangular parallelepiped
Delivered:
Straight SS 1 is perpendicular to the area ABC, and hence, straight AC. This means that the tricycle SS 1 A is rectangular. According to Pyfagor's theorem:
Rectangular tricycle ABC is clearly visible. According to Pyfagor's theorem:
Ale ВС and AD - opposite sides of the rectangle. Hence, BC = AD. Todi:
So yak , a , That. Oskilki SS 1 = AA 1, then it will be necessary to bring it up.
Diagonals of rectangular parallelepiped pivni.
Apparently, vimіryuvannya parallelepipeda ABC yak a, b, c (div. Fig. 6), toodi AC 1 = CA 1 = B 1 D = D B 1 =
Theorem. Every parallelepiped has opposite edges and parallel edges.
So, between (Fig.) BB 1 C 1 C and AA 1 D 1 D parallel, that is, two intersecting straight lines BB 1 and B 1 З 1 one side parallel to two intersecting straight lines AA 1 and A 1 D 1 small. Ci between and є equal, so yak B 1 З 1 = A 1 D 1, B 1 B = A 1 A (yak opposite sides of the parallelogram) і ∠BB 1 С 1 = ∠AA 1 D 1.
Theorem. In every parallelepiped, all the diagonals are intertwined in one point and spread in different directions.
At the same time (Fig.) In parallel with two diagonals, for example, AC 1 and DB 1, and it is carried out straight AB 1 and DC 1.
So, as the edges AD and B 1 З 1 are similar and parallel to the edge BC, then the smell is equal and parallel to each other.
Occasionally, ADC 1 B 1 є parallelogram, in which Z 1 A and DB 1 - diagonal, and in the parallelogram the diagonal changes into navpil.
This can be proven to be repeated about the skin two diagonals.
To this, the diagonal AC 1 is overflowed from BD 1 navpil, diagonal BD 1 s A 1 S navpil.
In such a rank, all diagonals are intertwined into one point.
Theorem. In a rectangular parallelepiped square, be-diagonal squares in three squares.
Nekhai (Fig.) AC 1 є as the diagonal of the rectangular parallelepiped.
Having carried out AC, two tricycles are accepted: AC 1 С and ACB. The offense of the stench is straightforward:
First of all, it is parallel straight, and the same, the edge CC 1 is perpendicular to the base,
the other is that it is parallel rectangular, which means that it is rectangular in front of it.
3 tsikh trikutnik_v known:
AC 2 +1 = AC 2 + CC 2 1 і AC 2 = AB 2 + BC 2
From the same, AC 2 +1 = AB 2 + BC 2 + CC 2 +1 = AB 2 + AD 2 + AA 2 1
Slidstvo. In the rectangular parallelepiped all diagonals are.
Parallelepiped is a complete geometric figure, all 6 faces are parallelograms.
Fallingly in the form of cich parallelograms develop the onset of the parallelepiped:
- straight;
- abduction;
- rectangular.
A straight parallelepiped is called a chotiricut prism, the edges of which are folded with a 90 ° base area.
A rectangular parallelepiped is called a chotiricut prism, all sides of which are rectangular. The cube is a type of chotiricut prism, at which all faces and edges are rivni between themselves.
The peculiarities of the figurines zoom in on the power. Before them, there are 4 offensive tverdzhen:
The memory of all the induction of power is simple, the stench is easy for intelligence and to be seen logically in view of the peculiarities of the geometric body. However, it is simple and hard to be correct when you see typical buildings of the EDI and allow you to spare an hour, which is necessary for passing the test.
paralelepipeda formulas
For a joke of ideas on the establishment of a lack of nobility, only the power of the figuri. It is also possible to know and do the formulas for the meaning of the area and the shape of the geometric body.
The area is also located as an indicator of a parallelogram or a rectum. Vibrating from the parallelogram can be done independently. As a rule, when solving problems, it is simpler to use a prism, the basis of which is a rectangle.
The formula for the knowledge of the parallel surfaces of the parallelepiped can also be found in their tests.
Put on the design of typical buildings ЄDI
Zavdannya 1.
given: Rectangular parallelepiped with vimirs 3, 4 and 12 cm.
necessary to know the dinner of one of the head diagonals of the figuri.
Decision: Be it the decision of the geometric design guilty to try to induce the correct and clean chair, on which the "given" and the shukan value is signified. On the little bottom of the guidance, the butt of the correct registration of the minds.
Having looked at the ruptures of the little ones and having guessed all the powers of the geometric body, we come to the one true way of seeing. Having become obstinate 4 the power of the parallelepiped, we can take such a viraz:
For awkward enumeration, we can take a viraz b2 = 169, then, b = 13. According to the knowledge, for one move and a chair, vitratity should not be more than 5 quills.
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a, aside from the submission of the PP;
z th height.
- scho it is necessary to know, like tribute to mi maєmo?
- What is the power of the rectangular parallelepiped?
- stuck here Pyfagor's theorem? Yak?
- Sufficient tribute for storing the Pythagorean theorems, or the need for rosary?
diagonal square, Square parallelepiped (marvel at the power of a square parallelepiped) on the way to the sum of squares of the third and third sides (width, height, tovschina), and apparently the diagonal of the square parallel to the root
I will guess the school curriculum in geometry, you can put it like this: the diagonal parallel to the square root of all three sides of the sum of all three sides (the stink of small letters a, b, c).
Dovzhina diagonal rectangular parallelepiped to the square root from the sum of the squares on the side.
As soon as I don’t have mercy, and if I don’t remember, then the diagonal of the rectangular parallelepiped is equal to the root of the square sum of the squares of all three sides.
a square of diagonal roads, a sum of squares of width, a height and a dovzhini, in accordance with the common formula, we can accept it, a diagonal root square with a sum of three different sizes, letters in abc I mean
A rectangular parallelepiped (PP) є nі scho іnshe, yak a prism, before yakіy rectangular. At PP, all diagonals are equal, meaning be-like yogo diagonal rozrakhovuєtsya for the formula:
It is possible to give and іnshe value, looking at the Cartesian rectangular coordinate system:
Diagonal PP is a radius vector of a point to space, given by coordinates x, y and z in a Cartesian coordinate system. Tsei radius vector to the point is drawn from the cob of coordinates. And the coordinates of the point will be the projection of the radius vector (diagonal PP) on the coordinate axis. The projections are built from the peaks of this parallelepiped.
The rectangular parallelepiped is a type of dwarf sided, which folds from 6 faces, at the base of which is a rectangular one. Diagonal - tse vіdrizok, which is the opposite of the vertex of the parallelogram.
The formula for knowing diagonals is the square of the diagonal of the two squares of the three dimensions of the parallelogram.
Known in the Internet there is a bad scheme-table with overdrawn for everything, є in parallel. Є formula, how to know the diagonal, how to mean d.
Є The image of the boundary, the pinnacle and the most important speeches for parallels.
If the rectangular parallelepiped has a dovzhin, height and width (a, b, c), then the formula for the size of a diagonal will look like this:
Call your readers not to misunderstand your scholars naked; the formula, and they could report it, so they could independently її ї ї ї її to learn, asking the power supply:
Call for feedback on the supply of food, research without a proper way to give the formula.
Diagonals of rectangular parallelepiped pivni. It is also the same as the diagonal of the other edges. Dovzhinu diagonal can be counted, I know evenin the edges of the parallelogram, which go from one vertex. Qia dovzhina to the square root iz sumi squares dovzhin yogo rber.
The rectangular parallelepiped is one of the so-called bogatogranniks, which folds into 6 faces, the skin of which is rectangular. And the diagonal is the center of the edges, which is the opposite of the vertex of the parallelogram. As soon as the width and height of the rectangular parallelepiped are taken as a, b, c for as long as possible, then the formula of the diagonal (D) will be the next step: D ^ 2 = a ^ 2 + b ^ 2 + c ^ 2.
Diagonal rectangular parallelepiped- tse vіdrizok, scho from the one opposite peak Otzhe, we have є rectangular parallelepiped from the diagonal d and from the sides a, b, c. One of the powers of the parallelepipeda to say that the square dozhini diagonal d dorіvnyu sumy squares TPX yogo vimіryuvan a, b, c. Zvidsi visnovok, scho dovzhina diagonal can be easily insured for the offensive formula:
