3.6 Parallelograms
Unlike trapezoids, which are quadrilaterals with only one pair of opposite sides as parallel, if both the pairs of opposite sides are parallel, the quadrilateral is called a parallelogram. Figure 3.14 is a parallelogram.
Figure 3.14
Seg.AB is parallel to seg.DC i.e. Seg. AB çç
seg.DC and seg.AD is parallel
to seg.BC i.e. seg.AD çç
seg.BC. Therefore ABCD is a parallelogram. It is
represented as parallelogram ABCD. Since both sides the are parallel,
a parallelogram has two pairs of bases and hence two attitudes.
Properties of Parallelograms
Theorem: The opposite sides of a parallelogram
are congruent. Figure 3.15 shows a parallelogram ABCD to prove that
seg.AB @ seg.CD
& seg.AD @ seg.BC.
Figure 3.15
Join A to C. Consider the two triangles D
ACB and D CAD.
Ð CAB @
Ð ACD ( alternate angles )
Ð ACB @
Ð CAD ( alternate angles )
and seg.AC @ seg.CA ( same
side )
\ D
ACB @ D
CAD ( ASA )
\ seg.AB @
seg.CD and seg.CB @ seg.DA as
corresponding sides of congruent angles are congruent.
