Question

Complete the attached “Isosceles Proof” using the two-column proof provided

Answer 1

It can now be “taken for granted” that angle BAD and angle CAD are equal. Hence we can state that the line AD is an angle bisector of angle BAC.

Therefore, we know that BD = DC and AD is the perpendicular bisector of BC. By using the property angle sum of ∆ = 180˚, we can say that angle ABD is equal to angle ACD. Hence, by the converse of base angles of isosceles triangles, we can conclude that ∆BAC is an isosceles triangle. (Hence Shown)