If a line parallel to one side of a triangle intersects the other two sides in two distinct points, then the other two sides are divided in the same ratio by it.
The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
The opposite angles of a cyclic quadrilateral are supplementary.
If a secant and a tangent of a circle intersect in a point outside the circle then the area of the rectangle formed by the two line segments corresponding to the secant is equal to the area of the square formed by line segment corresponding the tangent.
The lengths of the two tangents segments to a circle drawn from an external point are equal.
If the angles of a triangle are 45 degree, 45 degree, and 90 degree, then each of the perpendicular sides is (1/√2 ) times the hypotenuse.