In triangle ABC, bisector BD is drawn, angle A = 75 degrees, angle C = 35 degrees 1) Prove that triangle BDC

In triangle ABC, bisector BD is drawn, angle A = 75 degrees, angle C = 35 degrees 1) Prove that triangle BDC is isosceles 2) Compare the segments AD and BC.

1)

Determine the value of the angle CBA.

Angle CBA = 180 – AСB – BAC = 180 – 35 – 75 = 700.

Since BD, by condition, is the bisector of the angle ABC, then the angle CBD = ABD = ABC / 2 = 70/2 = 35.

In triangle ВСD, the angles at the base ВС are equal to 35, therefore triangle ВDC is isosceles, and DB = DC, which was required to be proved.

2)

Consider triangles BCD and ABD. In triangle ABD, angle ADB = 180 – 30 – 75 = 750.

Triangles BCD and ABD are isosceles with the same sides. BD = CD = BD = ВA.

Let’s compare the bases BC and AD. The base CD lies against the angle 75, and the base AD is against the angle 30, therefore BC> AD.

Answer: ВС> АD.