Conjectures 1 - Perpendicular Bisectors
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?
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?
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.