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Add 4 matchsticks to divide the triangle into 3 equal parts. The 3 parts may differ in shape but must be equal in size.
If the length of 1 matchstick is 1 unit, the size of the big triangle (A + B + C + D) is:
= 1/2 X 4 X 3
= 6 square units
The size of rectangle A is:
= 2 X 1
= 2 square units
The size of triangle B is:
= 1/2 X 1 X 2
= 1 square unit
But C = B based on the same calculation which results in B + C = 2 square units.
Size of part D is:
= Big triangle - size A - size B - size C
= 6 - 2 - 1 - 1
= 2 square units
It should be clear that A = D = (B + C)
= 1/2 X 4 X 3
= 6 square units
The size of rectangle A is:
= 2 X 1
= 2 square units
The size of triangle B is:
= 1/2 X 1 X 2
= 1 square unit
But C = B based on the same calculation which results in B + C = 2 square units.
Size of part D is:
= Big triangle - size A - size B - size C
= 6 - 2 - 1 - 1
= 2 square units
It should be clear that A = D = (B + C)
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