In Math figures are said to be identical if two conditions are satisfied, that are:
1. They both possess the same shape which can Mean corresponding angles of two shapes are equal.
2. The sides of two shapes change by equal scale factor which can mean that all edges of one figure when scaled by a constant factor then second figure is obtained. Same happens when sides of second figure are scaled by some constant factor then we get 1st figure.
Let us learn how to find scale factor of two rectangles with help of an example:
Q. Suppose we have two rectangles as follows:
Find their scale factor?
Solution: It is clear from two figures that when we evaluate the scale factor from 1st figure to 2nd figure we get: 2 (4 * 2 = 8; 6 * 2 = 12). Sides of 2nd figure are attained by multiplying the sides of 1st figure by 2.
Similarly, when we evaluate the scale factor from 2nd figure to 1st figure we get: 1 /2 (8 * 1 /2 = 4; 12 * 1 /2 = 6). Sides of 1st figure are attained by multiplying the sides of 2nd figure by 1 /2. Thus we see scale factors for sides of two rectangles are reciprocal of each other. If we consider the scale factor of perimeter and area we get:
Area of 1st figure (24) * 4 = Area of the 2nd figure (96) or,
Area of 1st figure (24) =1 /4 * Area of the 2nd figure (96),
Perimeter of 1st figure (20) * 2 = Perimeter of the 2nd figure (40) or,
Area of 1st figure (20) =1 /2 * Area of the 2nd figure (40).