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Conjectures 1 - Perpendicular Bisectors

Author:Ms. Orr
In an earlier activity, we established the definition of Perpendicular. Definition: Bisect - to divide into two equal pieces. Definition: Perpendicular Bisector - If a line (or ray or segment) is perpendicular to a segment and also bisect that segment, then it is a perpendicular bisector of that segment. Definition: Equidistant - of equal distances.
Each of the tasks/diagrams below shows slightly different scenarios, but in all of them line CM intersects segment AB at point M and d1 refers to the distance from C to A while d2 refers to the distance from C to B. Use your spatial intuition in conjunction with these diagrams to answer the questions below. INSTRUCTIONS FOR TASK: Scenario 1: If CM is perpendicular to AB, but M in NOT the midpoint of AB, does it seem like d1 and d2 will be equal? STEP 1: Move point C below, make some observations, and answer the question below the applet.

REFLECT: If CM is perpendicular to AB, but M in NOT the midpoint of AB, does it seem like d1 and d2 will be equal?

INSTRUCTIONS FOR TASK: Scenario 2: If M is the midpoint of AB, but CM is NOT perpendicular to AB, does it seem like d1 and d2 will be equal? STEP 1: Move point C below, make some observations, and answer the question below the applet.

REFLECT: If M is the midpoint of AB, but CM is NOT perpendicular to AB, does it seem like d1 and d2 will be equal?

INSTRUCTIONS FOR TASK: Scenario 3: If M is the midpoint of AB and CM is perpendicular to AB, does it seem like d1 and d2 will be equal? STEP 1: Move point C below, make some observations, and answer the question below the applet.

REFLECT: If M is the midpoint of AB and CM is perpendicular to AB, does it seem like d1 and d2 will be equal?

REFLECT: Step 2: In Task 3 above, add another point E on CM (the perpendicular bisector of AB). What do you notice about the distance E is from A and E is from B (in other words how do the lengths of EA and EB compare)? If you move point E along the bisector of AB, does that length relationship change?

Let's formalize this idea. Fill in the blank. Make sure to add this conjecture/theorem to your worksheet. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, the this point is _____________________ from the endpoints of that segment.

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