Mathematics

In the figure, AB=CD.Prove that BE=DE and AE=CE where E is the point of intersection of AD and BC.


SOLUTION
In $$\triangle{EAB}$$ and $$\triangle{ECD}$$
$$AB=CD$$   [Given]
$$\angle{B}=\angle{D}$$   [Angles in the same segment]
$$\angle{A}=\angle{C}$$   [Angles in the same segment]
$$\therefore \triangle{EAB}\cong\triangle{ECD}$$    [ASA criteria]
$$\therefore BE=DE$$       [CPCT]
and $$AE=CE$$    [CPCT]
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