2. In the following figure, ABCD is a parallelogram and BD is a diagonal. Find the
value of r degree
C
or
39
7p
5p
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Answer:
Consider the diagram given in the question.
As we know, the diagonals of a parallelogram bisect each other.
Therefore,
⇒AC and BD bisect each other at point O.
Thus,⇒OA=OC and OB=OD
Now, consider points P and Q.
⇒BP=PQ=DQ ---- (1)
(1)Now, since OB=OD,
soPB+OP=OQ+DQFrom equation (1),
DQ+OP=OQ+DQ∴OP=OQ
Thus, AC and PQ bisects each other.
Thus, APCQ is a parallelogram, because both the diagonals bisect each other. Also, since, CQ and AP are the opposite sides of the parallelogram APCQ, they are parallel to each other.
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