Question

Draw perpendicular bisectors of all the three sides of the triangle given below.
Please draw or take a pic of your answer
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Answer 1

Given :  A triangle

To Find : Draw perpendicular bisectors

Solution:

Construct perpendicular bisectors

Step 1 : Label the vertices as A , B and C

Step 2 : Using suitable compass width and taking A as center Draw arc on both sides of AB

Step 3 : Keeping compass width same and taking B as center Draw arcs on both sides intersecting arc drawn in previous step at M & N

Draw a line passing through M & N which is perpendicular bisector of AB

Similarly  draw perpendicular bisector of AC & BC

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Answer 2

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CONSTRUCTION: In triangle ABC , OQ & OR the perpendicular bisectors of sides BC & AC respectively, intersecting at point O. P is the mid point of AB.

TO PROVE THAT: OP is also a perpendicular bisector of AB. In that case , we can say that all 3 perpendicular bisectors are concurrent.

PROOF:

Since any point on the perpendicular bisector of any segment is equidistant from the end points of the segment. ( theorem proved by SAS congruency) . And also the converse of this theorem is true & can be proved by SAS congruency)

=> OB = OC

And also OC = OA

So, by above 2 statements, OB = OA. ………(1)

Also, PB = PA ( as P is the mid point of AB , by construction)

Hence, O & P both lie on the perpendicular bisector of AB. ( as these points are equidistant from A & B)

=> OP is the third perpendicular bisector of the triangle.

=> All 3 perpendicular bisectors have common point O.

Hence, these 3 are concurrent

[ Hence Proved]