The trapeze represents a quadrangle with two parallel parties. These parties are called the bases. Their final points are connected by pieces which are called sides. At an isosceles trapeze the sides are equal.

## It is required to you

- - isosceles trapeze;
- - lengths of the bases of a trapeze;
- - trapeze height;
- - sheet of paper;
- - pencil;
- - ruler.

## Instruction

1. Construct a trapeze according to statements of the problem. Several parameters have to be given you. As a rule, it is both bases and height. But also other conditions — one of the bases, its inclination to it of side and height are possible. Designate a trapeze as ABCD, the bases let will be an and b, designate height as h, and sides — x. As a trapeze isosceles, sides at it are equal.

2. From tops of B and S carry out heights to the lower basis. Designate points of intersection as M and N. To you two rectangular triangles — AMB and CND turned out. They are equal as under the terms of a task their hypotenuses are equal to AV and CD and also legs of BM and CN. Respectively, pieces of AM and DN are also equal among themselves. Designate their length as y.

3. To find length of the sum of these pieces, it is necessary from length of the basis of a to subtract b basis length. 2u =a-b. Respectively, one such piece will be equal to the difference of the bases divided on 2. y=(a-b)/2.

4. Find length of side of a trapeze which at the same time is also a hypotenuse of a rectangular triangle with legs known to you. Calculate it on Pythagorean theorem. It will be equal to a square root from the sum of squares of height and the difference of the bases divided on 2. That is x= √ y2+h2= √ (a-b)2/4+h2.

5. Knowing height and a tilt angle of side to the basis, make the same constructions. The difference of the bases in this case does not need to be calculated. Use the theorem of sine. The hypotenuse is equal to length of a leg increased by a sine opposite to it a corner. In this case x=h*sinCDN or x=h*sinBAM.

6. If you were given a trapeze side tilt angle not to lower, and to the top basis, find the necessary corner, proceeding from property of parallel straight lines. Remember one of properties of an isosceles trapeze according to which corners between one of the bases and sides are equal.