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What happens to the area of triangles formed in a rectangle when both diagonals are drawn?
- a)They become smaller
- b)Their areas depend on their angles
- c)They have equal areas
- d)They become larger
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What happens to the area of triangles formed in a rectangle when both ...
Let the rectangle be ABCD and the diagonals AC and BD intersect at O.
In a rectangle (a parallelogram) the diagonals bisect each other; hence O is the midpoint of both AC and BD.
The diagonals divide the rectangle into four triangles whose total area equals the area of the rectangle. By symmetry and because opposite triangles are congruent, all four triangles have the same area.
Therefore, each triangle has equal area (each is one quarter of the rectangle's area).
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