Which construction could be used to construct an isosceles triangle ABC given line segment AB?

A)
Mark a third point C not on segment AB. Draw segments AC and BC.

B)
Label a point C on segment AB and construct a line perpendicular to AB through point C. Draw segments AC and BC.

C)
Construct the perpendicular bisector of segment AB. Mark the intersection of this line and AB and label it C. Draw segments AC and BC.

D)
Construct the perpendicular bisector of segment AB. Mark any point C on the perpendicular bisector except where it intersects AB. Draw segments AC and BC.

Construct the perpendicular bisector of segment AB. Mark any point C on the perpendicular bisector except where it intersects AB. Draw segments AC and BC.

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Explanation:

We start off with segment AB.

Let D be the midpoint, so that AD = DB

The perpendicular line through D is known as the perpendicular bisector. The term "bisect" means to "split in half".

Then we'll place point C anywhere along this new line, as long as it's not at point D's location.

This then helps us form segments AC and BC which are equal in length. This guarantees we have an isosceles triangle since we have 2 sides that are the same length.

Check out the diagram below.