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Example 2

PQRS is a parallelogram where A is the midpoint of PQ and B is the midpoint of SR. Prove that PABS is a parallelogram.

Solution:

Since A and B are both equidistant from seg.PS, seg.QR and seg.AB is parallel to seg.PS. Since seg.PQ çç seg.SR, seg.PA çç seg.SB. Therefore PABS is a parallelogram as both pairs of opposite sides are parallel.

Example 3

        ABCD is a parallelogram

          

      

Find length

Solution:

,   

Example 4

In a parallelogram ABCD, m Ð A = x0, m Ð B = ( 3x0 + 200 ), Find x, m Ð C and m Ð D.

Solution:

m Ð A + m Ð B = 1800

x0 + 3x0 + 200 = 1800

4x0 = 1600, x = 400

m Ð A = 400, m Ð B = 1400

Hence m Ð C = 400 and m Ð D = 1400

Example 5

Which of the following statements are true ?

a) Every rectangle is a parallelogram

b) Every rhombus is a rectangle

c) Every square is a rhombus

d) Every rectangle which is a rhombus is a square.

e) Every square is a parallelogram

f) The diagonals of a parallelogram are congruent.

Solution:

a) True

b) False

c) True

d) True

e) True

f) False

**********

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

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