# how do you prove that a bisector of a line segment is perpendicular to the line segment.?

i know that when you use a compase and everything else you get a bisector. to prove the bisector is perpendicular to the segment, you need to connect 2 triangles. i am not sure. please try to explain how to solve it.

### 2 Answers

- MaverickLv 71 decade agoFavorite Answer
Assuming you have line segment AB. For bisecting the line, you swing an arc from A and one from B. Looking only at the top side of the line segment, let's say that the segments meet at point C, and at point D below the line segment. You connect C and D and it crosses and bisects the line at point E.

OK, here we go.

AC = BC because arcs were same lenght

AE = BE bi-segments are of equal length

EC= EC identity

you now have a congruent triangles using side-side-side

angles AEC and BEC are supplementary (share common side and form straight line)

since they are congruent and add up to 180 degrees, they must be right angles

- 1 decade ago
you basically just need 2 say that the two angles are 90 degrees like where the bisector and the line meets.