Question

Construct an equilateral triangle with sides 5 cm and justify the construction.
Construct perpendicular bisectors of all sides and angle bisectors of all angles of
the same triangle. Write the inference of your observation.​

Answer 1

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 : 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 all intersects at same point

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Answer 2

Answer:

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Step-by-step explanation:

Let's assume side of equilateral triangle is 5.5 cm.

Steps of construction :

1) Draw a line segment AB of length 5.5 cm.

2) Taking 5.5 cm as radius, and A as centre, draw an arc.

3) Taking 5.5 cm as radius, and B as centre, draw another arc.

4) Let C be the point where the two arcs intersect . Join AC and BC and label the sides.

Thus, △ ABC is the required equilateral triangle.

Justification :

By construction, AB = AC = BC (Radius of equal arcs)

Since, all sides are equal , therefore, △ ABC is an equilateral triangle.