Because AB is perpendicular to BD and CD is perpendicular to BD.

So angle ABD= angle CDB = angle RT.

BD=BD

AD = BC

So the triangle ABD≌CDB(HL)

So AB=CD

Solution 2: It is easy to prove triangle ABF≌ triangle DCE(HL)

So BF=CE

BE=BF-EF

CF=CE-EF

So BE=CF

Solution 3: Because DE is vertical AB DF is vertical AC, DE=DF.

So AD is the bisector of the angle BAC

And because of the high AD.

So AD is vertical to BC.

So triangle ABC is an isosceles triangle

So AB=AC

4 solution: suppose that AC and BD intersect at point O, and it is easy to prove triangle DAB≌ triangle CAB(HL).

So AD=CB angle DBA = CAB angle

So OB=AO

So the triangle knife ≌ triangle (HL)

So DO=CO, so angle 1= angle 2.