In quadrilateral , sides and have equal length and are parallel to each other. Point is the intersection of the diagonals and How many pairs of congruent triangles are in the figure? (The figure below is not drawn to scale.)
Since AB and DC are parallel, quadrilateral ABCD is a parallelogram. Thus AC and BD bisect each other at P (in other words, AP=CP and BP=DP). Also, AP+BP=AB and CP+DP=DC, so AP=CP and BP=DP.
We can now pair up congruent triangles:
△ABD≅△CDA (by SAS)
△ADP≅△BCP (by SAS)
Thus there are 2 pairs of congruent triangles in the diagram.