Prove that median from the vertex of an isosceles Triangle is the bisector of the vertical angle

Prove that the median from the vertex of an isosceles triangle is the bisector of the vertical angle.

Prove that of all the triangles with a given base and a given vertex angle, an isosceles triangle has the greatest bisector of the vertex angle.

One of the base angles of an isosceles triangle is 70^(@) . The vertical angle is

Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.

Prove by vector method that median to the base of an isoscels triangle is perpendicular to the base.

Prove that the medians to the two equal sides of an isosceles triangle are equal.

Show that the bisector of vertical angle of an isosceles triangle bisects the base at right angles.

Show that the bisector of vertical angle of an isosceles triangle bisects the base at right angles.

Prove the following by vector method. Median to the base of an isosceles triangle is perpendicular to the base.

Prove using vectors: The median to the base of an isosceles triangle is perpendicular to the base.