Answer:

①∠BAD=∠ACD

It can only be concluded that ∠BAC is a right angle.

②∠BAD=∠CAD

Solution: Because AD⊥BC

So ∠ B = 90-∠ Bad, ∠ C = 90-∠ CAD.

And because ∠BAD=∠CAD.

So ∠ b = ∠ c.

So AB=AC, that is, △ABC is an isosceles triangle.

③AB+BD=AC+CD

Solution: Because AD⊥BC

So △ABD and △ACD are right triangles.

So AB? =AD？ +BD？

,

AC？ =AD？ +CD？

that is

AB？ -BD？ =AD？

,

AC？ -CD？ =AD？

that is

AB？ -BD？ =AC？ -CD？

That is, (AB+BD)(AB-BD)=(AC+CD)(AC-CD)

because

AB+BD=AC+CD①

therefore

AB-BD=AC-CD②

①+② The day after tomorrow.

AB=AC

So △ABC is an isosceles triangle.

④AB-BD=AC-CD

Solution: Get (AB+BD)(AB-BD)=(AC+CD)(AC-CD) in the same way as in ③.

because

AB-BD=AC-CD①

therefore

AB+BD=AC+CD②

①+② The day after tomorrow.

AB=AC

So △ABC is an isosceles triangle.