Question

直线a经过正方形ABCD的顶点A，分别过顶点B、D作BE⊥a于点E、DF⊥a于点F，若BE=4，DF=3，求EF的长及正

Answer 1

（1）∵ABCD是正方形∴AD="AB," ∠DAB=90°

∵BE⊥a, DF⊥a∴∠AEB=∠DFA=90°

∵∠EAB+∠ABE=∠FAD+

∠EAB=90°∴∠ABE=∠FAD

∴△ABE≌△AFD∴AF="BE=4,AE=DF=3" ∴EF="7"

（2）∵∠AEB=90°由勾股定理得：AB="5,"

略