1.

In the given figure, ABCD is a parallelogram. The quadrilateral PQRS is exactly(a) a square (b) a parallelogram (c) a rectangle (d) a rhombus

Answer»

(c) 

In parallelogram ABCD, ∠A+∠D = 180° 

⇒ In ΔASD,∠ADS +∠SAD = \(\frac{180°}{2}\) = 90° 

(∵ DS and AS bisect ∠s D and A respectively) 

∴ ∠ASD = 180° – ( ∠ADS + ∠SAD) 

= 180° – 90° = 90° 

⇒ ∠PSR = 90° (vert. opp. ∠s)

Similarly we can show that ∠SPQ = ∠PQR 

=∠QRS = 90°. 

∴ Quadrilateral PQRS is a rectangle.


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