The isosceles trapeze is a flat quadrangle. Two parties of a figure are parallel each other and other two sites of perimeter — sides are called the trapeze bases, and in case of an isosceles trapeze they are equal.
It is required to you
- - pencil
- - ruler
Instruction
1. Draw the sketch of an isosceles trapeze. Lower from tops on the top basis perpendiculars on the lower basis. The initial figure is put from a rectangle and two rectangular triangles now. Consider these triangles. They are equal as they have equal legs (perpendiculars between the parallel bases of a trapeze) and hypotenuses (sides of an isosceles trapeze).
2. Follows from equality of the considered triangles that all their elements are equal. But triangles are a part of a trapeze. Means, corners at the big basis of an isosceles trapeze are equal. This statement is useful for creation of the subsequent proof.
3. Again draw an isosceles trapeze. Carry out diagonal to trapezes and consider the triangle formed by trapeze side, its big basis and the carried-out diagonal. Carry out the second diagonal and consider one more triangle formed by the big basis, the second side and the second diagonal of a trapeze. Compare the considered triangles.
4. At the considered figures the big basis of a trapeze is the general party. Means, in triangles on two equal sides. On the basis of the statement proved in Paragraph 2 corners between respectively equal parties of triangles are equal. On the first sign of equality of triangles, the considered figures are equal. Therefore also their third parties which are diagonals of an isosceles trapeze are equal. At the further solution of geometrical tasks the equality of diagonals of an isosceles trapeze can be applied as already proved property of this figure.