如图,E为矩形ABCD内一点,且EB=EC,求证:AE=ED.

问题描述:

如图,E为矩形ABCD内一点,且EB=EC,求证:AE=ED.

∵四边形ABCD是矩形,
∴AB=CD,∠ABC=∠BCD,
∵EB=EC,
∴∠EBC=∠ECB,
∴∠ABE=∠ECD,
∴△ABE≌△DCE,
∴AE=ED.