The Converse of the Midpoint Theorem states that if a line segment is bisected by a perpendicular segment, then the two resulting segments are congruent. In oth...
The Converse of the Midpoint Theorem states that if a line segment is bisected by a perpendicular segment, then the two resulting segments are congruent. In other words, if AB ∩ CD = CD ∩ AB, then |AB| = |CD|.
This theorem can be proven using the following steps:
Assume that AB ∩ CD = CD ∩ AB.
Draw the perpendicular segment CD.
Since AB ∩ CD = CD ∩ AB, we have congruent triangles ABD and CBD.
By the transitive property of congruence, we have |AB| = |CD|.
The Converse of the Midpoint Theorem can be used to prove a variety of other theorems, such as the Pythagorean theorem and the similarity of triangles