# geometry

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If all of the diagonals are drawn from a vertex of a quadrilateral, how many triangles are formed?

• geometry -

sheesh! - draw one. There's only one diagonal, making 2 triangles.

a quad has only 4 points. pick a vertex. 2 of the other points form the adjoining side, leaving only 1 point left to form a diagonal.

• geometry -

I looked at it a bit different.

Drawing the two diagonals, which intersect at one point, leaves us with 5 points, from which to choose any 3 to form a triangle
We can choose C(5,3) or 10 such triples,
BUT, two of the triplets are the 3 points that form the diagonals, they cannot form a triangle.

So number of triangles = 10-2 = 8

Count them to verify.

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