In an isosceles triangle ABC with base AB, the angle A = 60 (degrees) Prove that the bisector BN of the angle CBD adjacent to the angle B of the triangle is parallel to AC.
Triangle ABC is isosceles by condition, which means that
∠ B = ∠ A = 60 ° (angles at the base of an isosceles triangle).
Find the degree measure of the CBD angle adjacent to the corners B.
∠ CBD = 180 ° – ∠ B = 120 °.
∠ NBC = ∠ CBD / 2 = 60 ° (BN is the bisector of the CBD angle).
∠ ABN = ∠ NBC + ∠ B = 120 °.
We got that the angle ABN is 120 °, the angle A is 60 °, their sum is 180 °.
These two angles are one-sided with straight lines AC, BN and secant AB, their sum 180 ° is one of the signs of parallelism of straight lines.
Straight lines BN and АС are parallel, as required.
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