Logic behind Construction of a Perpendicular Bisector of a Line Segment

# Logic behind Construction of a Perpendicular Bisector of a Line Segment

• 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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