The triangle is called isosceles if two parties are equal in it among themselves. Equality of two parties provides the certain dependences between elements of this figure facilitating the solution of geometrical tasks.
Instruction
1. In an isosceles triangle two equal parties are called side, and the third is the triangle basis. A point of intersection of the equal parties — top of an isosceles triangle. The corner between the identical parties is considered a corner at top, and two others — corners at the triangle basis.
2. Are proved such properties of an isosceles triangle: - equality of corners at the basis, - coincidence carried out from top of a bisector, a median and height with an axis of symmetry of a triangle, - equality among themselves two other bisectors (medians, heights), - crossing of bisectors (medians, heights) which are carried out from corners at the basis in the point lying on a symmetry axis. Existence of one of these signs serves as the proof that a triangle isosceles.
3. Make sure of the validity of the given properties of an isosceles triangle. Fold double the rectangular sheet of paper, having combined edges. Cut off a part of the put leaf in a straight line between any points on the line of a bend and at one of edges. Develop the turned-out triangle. It is obvious that the line of a bend is an axis of symmetry and divides a figure into two absolutely equal parts. Cut edges on both parts of the put leaf are equal and are the parties of an isosceles triangle.
4. Specify basic data of a task. In any triangle with the parties of "a", "b", "with" and corners "α", "β", "γ" it is impossible to prove anything. Dependences between figure elements are important. If it is possible to reduce the known parameters to one of the listed communications, then it is possible to take a ravnobedrennost of a triangle for granted and to use this fact during the further decision.
5. What data are sufficient for an opportunity to draw a conclusion about a triangle ravnobedrennost? It is necessary to know one party and two corners or a corner and two parties, i.e. existence of communication between the linear and angular sizes is obligatory.