Tasks on finding of length of the parties are one of the most widespread it is aware of geometry. The algorithm of their decision depends on basic data, features of the considered figure.
It is required to you
- - notebook;
- - ruler;
- - pencil;
- - handle;
- - calculator.
1. The simplest tasks on finding of length of the parties are tasks with the known perimeter (it is the sum of lengths of all parties). For example, the perimeter of a parallelogram of ABCD is equal to 22 cm, AV = 4, to find VS. Since opposite groans are equal in a parallelogram, AV = CD = 4.
2. Decision: From here VS = (22 – (AV * 2)) / 2BC = (22 – (4*2)) / 2BC = 7
3. Also often tasks on finding of length of the parties through the area meet. For example, the area of a rectangle of ABCD is equal to 24 cm, AV = 3 cm, to find VS. Opposite groans are also equal in a rectangle therefore AV = CD = 3.
4. Decision: S (it is direct.) = a*vs = AV * VSOtsyuda VS = S/ABBC = 8
5. A special case of a rectangle is the square. The square is a rectangle which parties are equal among themselves, and corners between them make 90 degrees. If the area of a square is known, then it is possible to find length of its party. For example, S squares of ABCD = 64 см^2. To find AV.
6. Decision: S (quarter) = а^2а = Sa = 64a = 8
7. But if no area not perimeter, but only length of one of the parties is unknown, then the decision becomes complicated. For example, in ABC 1/2AC triangle = 4 cm, SAV corner = DIA, VM – the bisector equal of 10 cm. To find AV.
8. Decision: If SAV corner = to a corner of DIA, then AVS triangle – isosceles. And in an isosceles triangle the bisector is a median and height. Since VM – height, that corner of VMA = 90, from here AVM triangle – rectangular. In a rectangular triangle of a square of a hypotenuse it is equal to the sum of squares of legs (on Pythagorean theorem). Therefore, AV ^2 = AM ^2 + VM ^2АВ ^2 = 16 + 100AB = √116