Respuesta :

mhanifa

Answer:

See below

Step-by-step 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

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