Its opposite sides are equal and parallel.This means that a rectangle is a parallelogram, so: The word ‘rectangle’ means ‘right angle’, and this is reflected in its definition.įirst Property of a rectangle − A rectangle is a parallelogramĮach pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. The diagonals of a parallelogram bisect each other. Third property of a parallelogram − The diagonals bisect each other Hence AB = CD and BC = AD (matching sides of congruent triangles). The opposite sides of a parallelogram are equal. Most of the remaining proofs however, are presented as exercises, with an abbreviated version given as an answer. Second property of a parallelogram − The opposite sides are equalĪs an example, this proof has been set out in full, with the congruence test fully developed. Let ABCD be a parallelogram, with A = α and B = β. The opposite angles of a parallelogram are equal. The first property is most easily proven using angle-chasing, but it can also be proven using congruence. The three properties of a parallelogram developed below concern first, the interior angles, secondly, the sides, and thirdly the diagonals. This is not the easiest way to construct a parallelogram.įirst property of a parallelogram − The opposite angles are equal We extend AD and AB and copy the angle at A to corresponding angles at B and D to determine C and complete the parallelogram ABCD. For example, suppose that we are given the intervals AB and AD in the diagram below. To construct a parallelogram using the definition, we can use the copy-an-angle construction to form parallel lines. The word ‘parallelogram’ comes from GreekĬonstructing a parallelogram using the definition Thus the quadrilateral ABCD shown opposite is a parallelogram because AB || DC and DA || CB. We begin with parallelograms, because we will be using the results about parallelograms when discussing the other figures.Ī parallelogram is a quadrilateral whose opposite sides are parallel. It is true that ‘If a number is a multiple of 4, then it is even’, but it is false that ‘If a number is even, then it is a multiple of 4’. Remember that a statement may be true, but its converse false.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |