Question

N a piece of paper draw segment AB and its midpoint D.

Then draw the perpendicular bisector of segment AB and name it ine CD
|/n your journal, write a proof that shows that the distance of point C from endpoint A is the same with the distance of
point C from endpoint B, or in other words prove that CA=CB.​

Answer 1

By Side-Side-Side (SSS) property, CA = CB

Explanation:

Given: /AB/ and bisector /CD/.

Proof: CA = CB

But,

AD = BD (since D is the midpoint of AB)

<CDA = CDB (right angle property)

<CAD = CBA (congruent property of triangles)

Therefore;

Δ ACD = ΔBCD (congruence property)

`(AD)/(CD)` =
`(BD)/(CD)` (proportion of the sides of two congruent triangles)

Thus, by Side-Side-Side (SSS) property, CA = CB