Page 123 - NUMINO Challenge_C1

14 Areas of Congruent Shapes

Basic Concepts Areas of Overlapping Shapes

If two congruent squares overlap such that the vertex of one square is at the
center of the other square, the overlapping area is always 1 of a square.

4

Example Two pieces of square paper of equal size are placed such that they
overlap, with the vertex of one square at the center of the other
square. Using the concept of congruence, explain why the

overlapping area is always 1 of a whole square.
4

(A) (B) (C)

Class Notes

In pictures (A) and (B), since the squares can be (A) (B)
divided into four shapes that are congruent with
the overlapping shape, the overlapping area is

of one square.

From the center of the square paper, draw a line (C)
perpendicular to the sides and you will get triangles AOD
and COB. If you compare the two triangles, A
OD

Side OD and side OB are of the same length ,

the length of one side of the square. ADO and CBO BC

are both angles.

AOD and COB are both ( ).

So, triangle AOD and triangle COB are , since the length of one side and

the angles on both sides are the same.

Therefore, the overlapping region has an area that is of one square paper.

120 NUMINO Challenge C1