Question

What facts are required in order to conclude that m∠ADE = m∠ABC?

A)AD = DB and AE = EC

B) AB = DE and AC = BC

C) DE = 2 •(BC), AD = 2 •(AB), and AE = 2 •(AC)

D) The exterior angle of a triangle is equal to the sum of the two remote interior angles.

Answer 1

The correct option is;

DE = 2·(BC), AD = 2·(AB), and AE = 2·(AC)

Explanation:

Given that we have;

1) The side AD of the angle m∠ADE corresponds to the side AB of the angle m∠ABC

2) The side DE of the angle m∠ADE corresponds to the side BC of the angle m∠ABC

3) The side AE of the angle m∠ADE corresponds to the side AC of the angle m∠ABC

Then when we have DE = 2·(BC), AD = 2·(AB), and AE = 2·(AC), we have by sin rule;

AE/(sin(m∠ADE)) = 2·(AC)/(sin(m∠ABC)) = AE/(sin(m∠ABC))

∴ (sin(m∠ADE)) = (sin(m∠ABC))

m∠ADE) = m∠ABC).