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Two triangles can be formed by the diagonals of one vertex of a four-sided polygon.
1. Opposite sides are equal 2. it is a parallelogram 3. all 4 angles (at vertices) are 900 4. diagonals are equal in length 5. diagonals bisect each other 6. triangles formed by a diagonal and 2 sides (opposite side for each triangle) are congruent 7. among the four triangles that are formed by the 2 diagonals, the vertically opposite triangles are congruent 8. if length=breadth, then the rectangle is a square 9. perimeter of the rectangle = 2 * ( length + breadth) 10. area of rectangle = length * breadth
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Figure that are congruent are shapes are the same size and shape. So when two formed congruent triangles are both together they fit just right.
If the triangles are congruent and you match the hypotenera the right way, you can get a rectangle. If the triangles are not congruent, you can't even necessarily get a quadrilateral.