The main feature of a quadrangular trapeze is the parallelism of two of its parties called the bases and not parallelism of sides of a figure. In case these sides are equal on length, the trapeze is called isosceles.
Instruction
1. In the solution of the majority of tasks of definition of corners of a quadrangular trapeze any given properties of a figure are considered. At the same time results of tasks can be various because of variable basic data. If before the decision conditions are given that only two corners relating to the trapeze basis are known, the solution of a task comes down to the following actions: Define alphabetic values for a trapeze – MNOP, and call the known corners according to ∠NMP and ∠OMP. Values for these corners will equal: ∠NMP = an and ∠OMP = b. You need to calculate corners at the top basis of ∠MNO and ∠NOP.
2. Use property of a trapeze when the sum of both corners at side equals 180 °. In this case required corners: ∠MNO = (180 ° – a), and ∠NOP = (180 ° – b).
3. At other basic data – equalities of certain parties of a trapeze and the known value of one of corners – a set of actions according to the solution of a task can take the following form. Use the same designations for MNOP trapeze, only in this case set that its parties of MN and OP and also the top basis NO are equal on length among themselves. The carried-out diagonal of MO is with MP basis ∠OMP corner = page.
4. Considering that in MNO triangle two of its parties equal each other, it is isosceles and ∠NMO corners = ∠NOM = d, and ∠MNO corner = e. As the sum of all corners in a triangle equals 180 °, therefore (2d + e) = 180 °. As a result of e = (180 ° – 2d).
5. Using property of a trapeze about the sum of the corners adjacent to one party equal 180 °, define other formula (e + d + c) = 180 °. Then at e = (180 ° – 2d) the formula takes a form (180 ° – 2d + d + c) = 180 ° or c = d.
6. As a result you will find ∠NMO corners = d = c and ∠MNO = e = 180 ° – 2c. As the set trapeze is isosceles, according to its property the ravnobokost of its diagonal are equal and corners at both bases are respectively equal. ∠OPM = ∠NOP = 180 ° – 2c means.