Question

How do you prove that a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects? (Two-column proof is needed) Whoever gives me a satisfactory answer will be rewarded with more points. Please include picture for reference.

Answer 1

The measure of CA is equal to measure of CB or CA=CB by the Side Angle Side congruence postulate.

What is a perpendicular line?

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other, known as parallel lines.

We have a statement:

a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.

Consider the line segment AB, 

let D be the midpoint of AB, so AD=DB

CD ⊥ AB

The triangles CAD and CBA are congruent from the Side Angle Side congruence postulate:

AD = DB, CD is common and Angle CDA = angle CDB = 90°, as CD ⊥ AB

So CA=CB

Thus, the measure of CA is equal to measure of CB or CA=CB by the Side Angle Side congruence postulate.

Learn more about the perpendicular line here:

brainly.com/question/18271653

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