Question

Can someone please help. I'm offering a lot of points because this answer needs an explanation. Statement proof style would be helpful, but it's not totally needed

Answer 1

See below

Explanation:

Given

• ∠A ≅ ∠B and CD⊥AB

To prove

• CD bisects ∠ACB

Solution

As CD⊥AB, ∠BDC = ∠ADC = 90°

∠BDC ≅ ∠ADC

• ∠BCD = 180 - (∠BDC + ∠DBC)

and

• ∠ACD = 180 - (∠ADC + ∠DAC)

We can substitute ∠ADC with ∠BDC and ∠DAC with ∠DBC

Then we get same equation for ∠BCD and ∠ACD

Therefore ∠BCD = ∠ACD = 1/2∠ACB

It proves that CD bisects ∠ACB