The figure below shows line t, which intersects segment AB:
Segment AB is intersected by line t. Point C is on line t.
In the image above, line t is a perpendicular bisector and angle 4 is congruent to angle 6. Write a paragraph to prove that point C is equidistant from points A and B.
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First, draw segments AC and BC. Also, call the point of intersection of line t and segment AB, point D.
Then since point T is the perpendicular bisector of segment AB, point D is the midpoint of segment AB.
Segments AD and BD are congruent because D is the midpoint of segment AB.
Name angles 1 and 2 as shown below.
Angles 1 and 2 are right angles because the lines are perpendicular.
Angles 1 and 2 are congruent because all right angles are congruent.
Segment DC is congruent to segment DC because of reflexive property of congruence.
Using SAS, triangles ACD and BCD are congruent.
By CPCTC, sides CA and CB are congruent.
Point C is equidistant from points A amd B.
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