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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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.

Geometry
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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You need to prove triangles congruent and then use CPCTC.

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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. |dw:1438042325361:dw|
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.
Oh my gosh thank you so much your the first person to explain it to me while making sense thanks a lot.
You are welcome. I'm glad it makes sense to you .

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