Let’s convince ourselves that what we’ve conjectured about perpendicular bisectors must be true.

​

​Learning Goal

​

​

• I can explain why the Perpendicular Bisector Theorem is true.

• I can use the perpendicular bisector theorem and its converse to find a missing angle or side in an isosceles triangle.​

​

​Learning Targets

​

​auxiliary line

​

​An extra line drawn in a figure to reveal a hidden structure

​

For example, the line shown in the isosceles triangle is a line of symmetry, and the lines shown in the parallelogram suggest a way of rearranging it into a rectangle.

​parallelogram

​

​A quadrilateral in which pairs of opposite sides are parallel

​converse

​

​The converse of an if-then statement is the statement that interchanges the hypothesis and the conclusion. For example, the converse of "if it's Tuesday, then this must be Belgium" is "if this is Belgium, then it must be Tuesday."

​The Perpendicular Bisector Theorem and Its converse

• If a point is on the perpendicular bisector of a segment, then it must be the same distance from both endpoints of the line segment.

• If a point is the same distance from both endpoints of a line segment, then it must be on the perpendicular bisector of the segment.

​Perpendicular Bisector Theorem Proof

https://www.youtube.com/watch?v=ttZvFhEq6cg​