In a number of planimetric tasks it is required to construct a median. It is the piece connecting triangle top to the middle of the opposite side. Also a median call the straight line containing this piece.
It is required to you
- ruler
- compasses
- pencil
- eraser
Instruction
1. To carry out a median, it is necessary to connect triangle top to the middle of the opposite side. Therefore the main complexity of a task consists in finding of the middle of this party. How to find the middle of the party?
2. At once comes to mind to measure it by a ruler and to postpone a half from one of the ends - here and there will be a median! Exactly! But if we carry out the drawing, and accuracy even in half-millimeter is essential to us? That and it! It is necessary to resort to other, more exact way.
3. Compasses and a ruler will be necessary for us. We estimate length of our piece by eye and we open compasses at any length. The main thing that this length was more than a half of a piece. Now it is necessary to carry out two circles from the ends of the broken piece.
4. We put a compasses needle in one of the ends of a piece, we carry out a circle. We make the same for other end of a piece. Especially we are interested in points where these circles will be crossed. Therefore it makes sense to trace in places of crossing of circles them stronger.
5. So, we will find points of intersection of circles. It is visible that they lie on different sides of our piece. Now we will connect them among themselves. We see, a new piece it crosses the party of a triangle. It turns out that the point of intersection and is the exact middle of our piece. Having connected this point to opposite top, we will also receive a required median.
6. There is the third way even more difficult. In this case the ruler and compasses will also be necessary for us. Let us have a triangle of ABC. Let to the party of AC of this triangle us want to construct a median. That to make it, it is necessary to carry out two circles by the following rules. Around top of C it is necessary to carry out AB radius circle. And around top of A it is necessary to carry out BC radius circle.
7. We measure AB piece length. Now without changing position of legs of compasses, we draw a circle from Page top. We make the same for a piece of BC and top of A. We receive two circles. The point of their crossing needs to be connected to B top. Thus, we received a median.