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

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**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.

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**Example 3

ABCD is a parallelogram

Find length

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**Solution:

,

Example 4

In a parallelogram ABCD, m Ð A = x^{0}, m Ð B = ( 3x^{0} + 20^{0} ), Find x, m Ð C and
m Ð D.

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**Solution:

m Ð A + m Ð B = 180^{0}

x^{0} + 3x^{0} + 20^{0} = 180^{0}

4x^{0} = 160^{0}, x = 40^{0}

m Ð A = 40^{0}, m Ð B = 140^{0}

Hence m Ð C = 40^{0} and m Ð D = 140^{0}

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.

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**Solution:

a) True

b) False

c) True

d) True

e) True

f) False

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