Question

In an examination, ABC is an equilateral triangle and AD is the perpendicular
bisector to BC. Prove that
AADB =AADC.​

Answer 1

Answer:

Given: In ∆ ABC, AD is the perpendicular bisector of BC. To Prove: A ABC is an isosceles triangle in which AB = AC. ∴ AB = AC | C.P.C.T. ... (iv) AP is the perpendicular bisector of BC.

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Answer 2

Answer:

Data: In ∆ABC, AD is the perpendicular bisector of BC. To Prove: ∆ABC is an isosceles triangle in which AB = AC. Proof: In ∆ABC, AD is the perpendicular bisector of BC. ∴ BD = DC ∴ ∠ADB = ∠ADC = 90°. Now, in ⊥∆ADB and ⊥∆ADC, BD = DC (AD is the perpendicular bisector) ∠ADB = ∠ADC = 90° (Data) AD is common ∴ ∆ADB ≅ ∆ADC ∴ Angles opposite to equal sides of an isosceles triangle are equal. ∴ AB = AC ∴ In ∆ABC, If AB = AC, then ∆ABC is an isosceles triangle.Read more on Sarthaks.com - https://www.sarthaks.com/670788/in-abc-the-perpendicular-bisector-of-bc-show-that-abc-is-an-isosceles-triangle-in-which-ab