It is given that AD = AC is the midpoint of the segment DC. Therefore, DB = BC by the definition of the midpoint making the segment AB as a bisector. Additionally, ∠D is congruent to the angle ∠C by the definition of the vertical angle theorem. Triangle ΔADB is congruent to triangle ΔACB by SAS theorem.
Since angles like ∠ ABD and ∠ABC are a linear pair adding up to 180 and congruent by linear pair postulate. This means that the angle ABD and ABC each measures 90 degrees. Therefore, segment AB is perpendicular to segment DC by midpoint isosceles theorem making segment AB both as a bisector and perpendicular to the segment DC.
What is midpoint theorem?
Midpoint theorem defines the center point of a line segment which forms the triangle. And the sides of the triangle are equal with one side is parallel to the remaining sides.
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