Page 1 - LN-5

SAI INTERNATIONAL SCHOOL

CBSE CURRICULUM

Class: VI

LESSON NOTE-8.5

SUBJECT: Mathematics

CH: 8-PLAYING WITH CONSTRUCTIONS
SUBTOPIC: EXPLORING DIAGONALS OF RECTANGLES AND SQUARES

Consider a rectangle PQRS. Join PR and QS. These two lines are called the diagonals of the
rectangle.

Compare the lengths of the diagonals.
In rectangle PQRS, the right angles at P and R are referred to as opposite angles. The other
pair of opposite angles are the right angles at Q and S.
Observe that a diagonal divides each of the pair of opposite angles into two smaller angles.
In the figure, the diagonal PR divides angle R into two smaller angles which we simply call g
and h. The diagonal also divides angle P into ‘c’ and ‘d’.
Now, check that:
1. Are g and h equal?
2. Are c and d equal?
Measure them and identify pairs of angles that are equal.
Example:
Construct a rectangle where one of its sides is 5 cm and the length of a diagonal is 7 cm.
Solution:
Let us start with a rough diagram
Steps of Construction:
1. The base CD measuring length of 5 cm can be easily constructed.
2. Draw a perpendicular to line DC at the point C. Let us call this line l