Question

given: c is a point on the perpendicular bisector, l, of ab. prove: ac = bc. use the drop - down menus to complete the proof. by the unique line postulate, you can draw only one segment, drop - down. using the definition of drop - down, reflect bc over l. by the definition of reflection, c is the image of itself and drop - down is the image of b. since reflections preserve drop - down, ac = bc. angles orientation length

Explanation:

Step1: Draw segment CD

By the unique - line postulate, we draw the perpendicular bisector segment CD from C to AB.

Step2: Define reflection

Using the definition of reflection, we reflect BC over the perpendicular bisector l.

Step3: Identify image

Since l is the perpendicular bisector of AB, when we reflect BC over l, C is the image of itself and A is the image of B.

Step4: Use property of reflection

Reflections preserve length. So, since the length of BC is equal to the length of its image AC, we have AC = BC.

Answer:

AC = BC because reflections preserve length. The first blank can be filled with "CD" (the segment drawn from C to the mid - point of AB), the second blank with "reflection", the third blank with "A", and the fourth blank with "length".