Heart of Mathematics Proofs

Doing Mathematics without proofs is a sin.

Theorem #16
Any point on the right bisector of a line segment is equidistant from its end points.

Theorem #15
If three or more parallel lines make a congruent intercepts on a transversal , then they also intercept congruent segments on any other line that cuts them.

Theorem #14
The medians of a triangle are concurrent, and their point of concurrency is the point of trisection of each median.

Rational numbers:
Such numbers which can be written in the form of p/q ,where p,q are integers and q is not zero.

Theorem #01 (Related to Circles)
If a perpendicular is drawn from the centre to a chord of a circle, it bisects the chord.

Theorem #13
The line segment, joining mid-points of two sides of triangle is parallel to the third line and half as long.

Theorem #12
If one pair of opposite sides of a quadrilateral are congruent and parallel, it is paralellogram.

Theorem #11
Opposite sides and angles of a paralellogram are congruent, and diagonals bisect each other.

Theorem #09
If two angles of a triangle are congruent, the opposite sides to them are also congruent.

Corollary(Theorem #06)
An equilateral triangle is an equiangular triangle.

Corollary (Theorem #06)
In an isosceles triangle, the angles at the base are congruent.