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A diagonal is normally defined as a straight line joining a vertex of a polygon with any vertex other than an adjoining vertex (lines joining a vertex to an adjoining vertex would simply be a side of the polygon). Since a triangle has only got adjoining vertices, it has no diagonals. Since there are no diagonals, they cannot bisect one another.

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Q: Does diagonals of right angled triangle bisect each other?
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How many right angled triangle are possible if two diagonals are drawn within a square?

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