construct an equilateral triangle of side 5cm and justify the construction construct perpendicular bisector of all sides and angle bisectors of all angles of the same triangle.write the inference of your observation
Answers
Given : an equilateral triangle with sides 5 cm
To Find : Construct an equilateral triangle
Construct perpendicular bisectors of all sides and angle bisectors of angles of the same triangle.
Solution:
Step 1 : Draw a line segment B = 5 cm
Step 2 : Using compass width = 5 cm and taking A as center , draw an arc
Step 3 : Keeping compass width same and taking B as center draw an arc intersecting previous arc at C
Step 4 : Join AC & BC
equilateral triangle is constructed
Construct perpendicular bisectors
Using suitable compass width and taking A as center Draw arc on both sides of AB
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
Construct angle bisector
Using Suitable compass width and taking A as center draw arc intersecting AB at X & AC at Y
Using Suitable compass width and taking X as center draw an arc
Keeping compass width same and taking Y as center draw an arc intersecting arc drawn in previous step at Z
Draw a ray passing through AZ
AZ is angle bisector of angle A
Similarly draw angle bisector of B & C
Perpendicular bisector & angle bisector of equilateral triangle intersects at same point
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