free booknotes online

Help / FAQ




Win a $1000 or more Scholarship to college!


Please Take our User Survey


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.

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

Chapter 4

All Contents Copyright © All rights reserved.
Further Distribution Is Strictly Prohibited.


Search:
Keywords:
In Association with Amazon.com