NCERT Book Class 7 Mathematics (Part II) Chapter 6 Constructions and Tilings

6 CONSTRUCTIONS
AND TILINGS

6.1 Geometric Constructions
Eyes
Do you recall the ‘Eyes’ construction we did in Grade 6?

Of course, eyes can be drawn freehand, but we wanted to construct
them so that the lower arc and upper arc of each eye look symmetrical.
We relied on our spatial estimation to determine the two centres, A
and B (see the figure), from which we drew
A
the lower arc and upper arc respectively.
The arcs define a line XY that ‘supports’
the drawing though it is not part of the final
figure. We can start with this supporting line
and systematically find the centres A and B.
For the eye to be symmetrical, or for the
X Y
supporting line to be the line of symmetry, the
upper and lower arcs should have the same
radius. In other words, we must have AX = BX.
Since AX = AY and BX = BY, this means B
AX = AY = BX = BY