in triangle abc AD | BC and AD bisects angle A. prove that triangle ABD=~ACD .
also prove that triangle ABC is isosceles.
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Step-by-step explanation:
Consider Δ ADB and Δ ADC.
BD = CD as AD bisects BC.
∠BAD = ∠CAD because AD bisects ∠A
∠ADB = ∠ADC = 90° because AD is perpendicular to BC
Hence, by ASA (Angle, side, angle) property, ABD≅ACD
Now, because ΔADB≅ΔADC, AB equals to AC, hence ΔABC is isosceles.
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