Question

PQRS is a parallelogram. A & B are points. In PQ & RS such that AP = BR.
So intersects AB to O. PQ = 10 cm, PS = 6 cm, AO = 3 cm, find OB.

• A. 3
• B. 4
• C. 6
• D. 10

Answer 1

Answer: (A)

3

$\Rightarrow$ In given figure ABCD is a parallelogram.

$\Rightarrow$ A abd B are points on sides PQ and RS such that AP = BR. -- (1)

$\Rightarrow$ So, A and B are midpoints on sides PQ and RS.

$\therefore$ AQ = SB ----- (2)

$\Rightarrow$ In $△SBO$ and $△AQO$

$\Rightarrow$ $\angle 1=\angle 2$ [Alternate interior angles]

$\Rightarrow$ $SB=AQ$ [From (2)]

$\Rightarrow$ $\angle 3=\angle 4$ [Vertically opposite angle]

$\therefore$ $△SBO\cong △AQO$ [By ASA criteria]

$\Rightarrow$ So, we get $AO=OB$ [CPCT]

We have given $AO=3cm$

$\therefore$ $OB=3cm$