Question

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.

Answer 1

Is there a figure?

Answer 2

You need to prove triangles congruent and then use CPCTC.

Answer 3

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.

Answer 4

Segments AD and BD are congruent because D is the midpoint of segment AB.

Answer 5

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.

Answer 6

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.

Answer 7

Oh my gosh thank you so much your the first person to explain it to me while making sense thanks a lot.

Answer 8

You are welcome.
I'm glad it makes sense to you .