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.

Index

3. 1 Definition
3. 2 Terminology
3. 3 Sum Of Interior Angles Of A Polygon
3. 4 Sum Of Exterior Angles Of A Polygon
3. 5 Trapezoids
3. 6 Parallelogram
3. 7 Square, Rectangle And Rhombus