In a triangle ABC ∠ A = 40 °; ∠ B = 70 °. A straight line ВD is drawn through the vertex В

In a triangle ABC ∠ A = 40 °; ∠ B = 70 °. A straight line ВD is drawn through the vertex В so that ВС is the bisector ∠АВD. Prove that AC || BD.

Since BC is the bisector of the angle ABD, the value of the angle ABD = 2 * ABC = 2 * 70 = 140.

Extend straight line AB to point E. Angle DBE and ABD are adjacent angles, the sum of which is 180, then angle DBE = 180 – ABD = 180 – 140 = 40.

Then the angle CAB = DBE.

Since the straight lines AC and ВD intersect the straight line AE at the same angle, the straight line AC is parallel to BD, which was required to be proved.