As shown in the figure, in triangles ABC, AD⊥BC and D, AB+BD=DC. Why ∠ ABC = 2 ∠ C?

Extend CB to e, make BE=BA, and connect AE.

∴DE=BE+BD=AB+BD=CD

∵AD⊥BC

∴AD is the middle vertical line of EC AE=AC.

∴∠E=∠C

BE = BA

∴∠E=∠EAB

∴∠ABC=∠E+∠EAB=2∠E

∠∠E =∠C

∴∠ABC =2∠C

The solution to this kind of problem is to make up for each other's shortcomings, the first floor method is to make up for each other's shortcomings, and the prompt method is to make up for each other's shortcomings.