conditional statements statements in geometry

The locus of a point equidistant from two fixed points is the perpendicular bisector of the segment joining the two points. This theorem is proved in two parts. First prove that any point on the locus satisfies the condition..

"If both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram". The converse statement stated above is a necessary condition for a quadrilateral to be a parallelogram. Similarly, we may formulate the following two other conditions..

If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary..

If two lines intersect, then the vertically opposite angles are congruent..

If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary..

If two diagonals of a parallelogram are equal, it is a rectangle..

If in a parallelogram, the diagonals are equal and perpendicular, then it is a square..

The diagonals of a parallelogram bisect each other..

A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel..

The diagonals of a rhombus are perpendicular to each other..