It is one of three sufficient conditions for triangles to be congruent. Theorem 2 . The straight line that bisects the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Let the straight line AD bisect the vertex angle of the isosceles triangle BAC, so that the angles BAD, DAC are equal to one another. To see the proof, pass your mouse over the colored area.
AD therefore is the perpendicular bisector of the base.
In an isosceles triangle the angles at the base are equal to one another . If two angles of a triangle are equal to one another, then the sides opposite those angles will be equal to one another. This theorem is called the converse of the previous one. The hypothesis and conclusion are exchanged. Theorem 5 .