The geometry is completely constructed on theorems and proofs. To prove that any figure of ABCD is a parallelogram, it is necessary to know definition and signs of this figure.
Instruction
1. A parallelogram in geometry is called the figure with four corners at which the opposite sides are parallel. Thus, the rhombus, a square and a rectangle are types of this quadrangle.
2. Prove that two of the opposite parties are equal and parallel rather each other. In ABCD parallelogram the sign looks so: AB=CD and AB | | CD. Draw diagonal the EXPERT. The received triangles will be equal on the second sign. The EXPERT - the general party, corners of BAC and ACD, also as well as VSA and CAD, are equal as lying crosswise at parallel direct AB and CD (it is given in a condition). But as these crosswise the lying corners treat also the parties of AD and BC, means these pieces also lie on parallel straight lines, as was exposed to the proof.
3. Important proof elements that ABCD a parallelogram, are diagonals as in this figure when crossing in O point they are divided into equal pieces (AO=OC, BO=OD). Triangles of AOB and COD are equal as their parties in connection with these conditions and vertical angles are equal. It follows from this that and corners of DBA and CDB also as well as are equal to CAB and ACD.
4. But the same corners are crosswise lying while direct AB and CDs are parallel, and diagonal is served by a secant. Having proved in such a way that also two another triangles formed by diagonals are equal, you receive that the parallelogram given a quadrangle.
5. One more property on which it is possible to prove that ABCD quadrangle - a parallelogram sounds so: opposite corners of this figure are equal, that is the corner of B is equal to a corner of D, and the corner of C is equal to A. The sum of corners of triangles which we will receive if we carry out AC diagonal is equal 180 °. Proceeding from it we receive that the sum of all corners of this figure of ABCD is equal 360 °.
6. Having remembered statements of the problem, it is possible to understand easily that the corner of A and a corner of D in the sum will make 180 °, similar to a corner of C + a corner of D = 180 °. At the same time these corners are internal, lie on one party, at the straight lines corresponding to them and secants. From this it follows that straight lines of BC and AD are parallel, and the given figure is a parallelogram.