In all the following proofs it is important
a) to maintain the generality of the proof
b) to choose wisely the system of axes
Together:
1) Prove that all the points on the perpendicular bisector of a line segment AB are
equidistant from the endpoints of the segment.
2) Prove that if ABCD is a parallelogram (AB || CD and AD || BC ) then its diagonals bisect each other.
3) Prove that in any triangle ABC, the medians are concurrent.
Homework:
1) Prove that when connecting the midpoints of the sides of any quadrilateral one obtains a parallelogram.
2) Prove that if in a quadrilateral ABCD the diagonals bisect each other than the quadrilateral is a parallelogram.
(Hint: Choose the intersection of the diagonals as the origin of the axes.)
3) Prove that in any triangle ABC the altitudes are concurrent.
(Hint: Choose A(a,0), B(0,b), C (c,0).)
4) Prove that in any triangle ABC, the perpendicular bisectors of the sides are concurrent.