Page No 94.
1. Find all the other angles inside the following rectangles.
(i) 
∠1=∠2=∠5=∠6=∠AOD=∠BOC=60°
∠3=∠4=∠7=∠8=30°
∠AOB=∠COD=120°
(ii)
∠1=∠2=∠5=∠6=55°
∠3=∠4=∠7=∠8=35°
∠PSO=∠ROQ=110°
∠POQ=∠SOR=70°
2. Draw a quadrilateral whose diagonals have equal lengths of 8 cm that bisect each other, and intersect at an angle of
(i) 30°
(ii) 40°
(iii) 90°
(iv) 140°
(ii) 40°
(iii) 90°
(iv) 140°
Ans :
(i) 
(ii)
(iii)
(iv)
3. Consider a circle with centre O. Line segments PL and AM are two perpendicular diameters of the circle. What is the figure APML? Reason and/or experiment to figure this out.
Ans :
O is the centre of the circle.
PL and AM are two perpendicular diameters. So, OP = OL = OA = OM (all are radii).
The diagonals of quadrilateral APML are PL and AM. They bisect each other at O because O is the centre. They are equal because both are diameters of the same circle. They are also perpendicular.
A quadrilateral whose diagonals are equal, bisect each other, and are perpendicular is a square.
Therefore, APML is a square.
4. We have seen how to get 90° using paper folding. Now, suppose we do not have any paper but two sticks of equal length, and a
thread. How do we make an exact 90° using these?
Ans : Coming Soon.
5. We saw that one of the properties of a rectangle is that its opposite sides are parallel. Can this be chosen as a definition of a rectangle? In other words, is every quadrilateral that has opposite sides parallel and equal, a rectangle?
Ans : No. A quadrilateral with opposite sides parallel and equal is called a parallelogram, not necessarily a rectangle. A rectangle must also have all four angles equal to 90°. Therefore, this is not a complete definition of a rectangle.