If a segment bisects one side of a triangle and is parallel to another side, it bisects the third side as well.
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No, it does not.
The isosceles triangle theorem states that if two sides of a triangle are congruent, the angles opposite of them are congruent. The converse of this theorem states that if two angles of a triangle are congruent, the sides that are opposite of them are congruent.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle-apex
what is corner point theorem
angles that are in the formation of a F are equal if they are corresponding, the F sometimes isn't obvious