Question

In the following figure, ABCD is a parallelogram and BD is a diagonal. Find the value of r degree…

Answer 1

$\huge \sf {\orange {\underline {\pink{\underline {ANSWER☆ :-}}}}}$

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.

$\huge \mathbb \red {Hence \: proved \:}$

Answer 2

Answer:

\huge \sf {\orange {\underline {\pink{\underline {ANSWER☆ :-}}}}}

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.

\huge \mathbb \red {Hence \: proved \:}Henceproved