Perpendicular Bisector Theorem

​The Perpendicular Bisector Theorem

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

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

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​Learning Goal

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• 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.​

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​Learning Targets

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​auxiliary line

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

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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

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​A quadrilateral in which pairs of opposite sides are parallel

​converse

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​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."

Poll

Which one doesn’t belong?

• A

• B

• C

• D

Open Ended

What do you notice, What do you wonder?

​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.

Multiple Choice

What does the word BISECT mean?

• To cut something into more than two pieces

• It is an object on the plane with has two equal sets of parts.

• To cut something into two congruent pieces or in half.

• A shape that is created which has three equal sides. 

Multiple Choice

A point that is the same distance from two figures is ___________________ from the two figures.

• Congruent

• Corresponding

• Vertical

• Equidistant

​Perpendicular Bisector Theorem Proof

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

Multiple Choice

YW is the perpendicular bisector of XZ. Is triangle YWX≅ Triangle YWZ? If so how?

• no

• yes, SSS

• yes, SAS

• yes, ASA

Open Ended

What is the measure of $$\overline{AC}$$  

Multiple Choice

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

• True

• False

Multiple Choice

Find the length of AD

• 2

• 4

• 6

• 8