MathsPractical GeometryConstruction Perpendicular Bisector WhyLogic behind Construction of a Perpendicular Bisector of a Line Segment

Logic behind Construction of a Perpendicular Bisector of a Line Segment

Table of Contents

  • Logic behind Drawing a Perpendicular Bisector of a Line Segment
  • Summary
  • What’s Next?

In the previous segment of Class 6 Maths, we learnt how to draw a perpendicular bisector of a line segment. Here, let us learn about the logic behind it.

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    Logic behind drawing a perpendicular bisector of a line segment

    The construction of a perpendicular bisector of a line segment is as shown below:

    Construction of perpendicular bisector

    Let’s understand how the constructed line (line CD) is a perpendicular bisector of the given line

    segment (seg AB). That is, to ????? ???? ?? ⊥ ??? ?? ??? ??? ?? ≅ ??? ??.

    Join CA, CB, DA, and DB.

    Construction for proof

    No

    .

    Statement

    Reason

    1

    CA = CB = DA = DB

    The compass width used to draw the arcs was the same.

    ???????? △ ??? ??? △ ???.

    2

    ??? ?? ≅ ??? ??

    From statement 1

    3

    ??? ?? ≅ ??? ??

    From statement 1

    4

    ??? ?? ≅ ??? ??

    Common side

    5

    ∴△ ??? ≅△ ???

    By SSS test of congruency.

    6

    ∴ ∠??? ≅ ∠???

    Corresponding angles of congruent triangles are congruent.

    7

    ∴ ∠??? ≅ ∠???

    Corresponding angles of congruent triangles are congruent.

    ???????? △ ???

    8

    [?????]??? ?? ≅ ??? ??[/?????]

    From statement 1.

    9

    ∴ ∠??? ≅ ∠???

    Opposite angles of congruent sides are congruent in a triangle.

    ???????? △ ???

    10

    ??? ?? ≅ ??? ??

    From statement 1

    11

    ∴ ∠??? ≅ ∠???

    Opposite angles of congruent sides

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