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.
- 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.