That quickly and correctly to solve geometrical problems, it is necessary to acquire well that the figure or a solid about which it is and to know their properties represents. Some part of simple geometrical tasks is constructed on it.
Instruction
1. For a start it is necessary to remember what is a trapeze and what properties it has. The trapeze is a quadrangle which two opposite sides are parallel. The parallel parties are the trapeze bases, and two others – its sides. If sides of a trapeze are equal, then it is called equilateral. Corners at the bases of an equilateral trapeze are in pairs equal, i.e. the corner of AVS is equal to BCD corner, and the corner of BAD is equal to CDA corner.
2. Diagonals divide a trapeze into triangles. For the proof of equality of diagonals of an equilateral trapeze it is necessary to consider triangles of ABC and BCD and to prove that they are equal among themselves as diagonals the EXPERT and BD at the same time are the parties of these triangles.
3. The party of AV of a triangle of AVS is equal to side of CD of a triangle of BCD as they are at the same time sides of an equilateral trapeze (i.e. on a condition). The corner of AVS of a triangle of AVS is equal to BCD triangle BCD corner as they are the corners lying at the trapeze basis (property of an equilateral trapeze). The party of VS is the general for both triangles.
4. Thus, there are two triangles with two equal parties and equal corners concluded between them. Therefore the triangle of AVS is equal to BCD triangle on the first sign of equality of triangles.
5. If triangles are equal, then also their relevant parties, i.e. the party are equal the EXPERT is equal to the party of BD and as they at the same time are diagonals of an equilateral trapeze, their equality is proved.
6. For the proof it is possible to use triangles of ABD and ACD which are also equal among themselves on the first sign of equality of triangles. In this case the proof is similar.
7. The statement that diagonals are equal, is fair only for an equilateral trapeze.