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

  • 1 decade ago
    Favorite 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.

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