What is the Linear Pair Perpendicular Theorem? The median of an equilateral triangle is an example of a perpendicular bisector. The median of a triangle is the line that joins the vertex of the triangle to the midpoint of the opposite side of the vertex. What is an Example of a Perpendicular Bisector? The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle. The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn. What is the Perpendicular Bisector Theorem? How do You Know if Two Line Segments are Perpendicular?.Related Topics on Perpendicular Bisector Theorem The perpendicular bisector theorem is used in the construction of buildings, bridges, etc., and in making designs where we need to build something in the center and at equal distance from the endpoints.The perpendicular bisector theorem and its converse can be proved by the SAS congruency criterion.Thus, AD = BD, which means that C is equidistant from A and B. We see that \(\Delta ACD \cong \Delta BCD\) by the SAS congruence criterion. Now, compare \(\Delta ACD\) and \(\Delta BCD\). Perpendicular Bisector Theorem Converse Proofĭraw a perpendicular line from point C that intersects line segment AB at point D. Note: Refer to the SAS congruence criterion to understand why \(\Delta ACD\) and \(\Delta BCD\) are congruent. CA = CB,which means that C is equidistant from A and B. Perpendicular Bisector Theorem ProofĬonsider the following figure, in which C is an arbitrary point on the perpendicular bisector of AB (which intersects AB at D):Ĭompare \(\Delta ACD\) and \(\Delta BCD\). Let us look at the proof of the above two theorems on a perpendicular bisector.
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