Question

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

Answer 1

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Let's assume side of equilateral triangle is 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.

Answer 2

How do you construct an equilateral triangle with a side of 5 cm?

1. Draw AB as base = 5 cm.........
2. Draw perpendicular bisector of AB.......
3. Open the compass for 5 cm, keep the pointer at A and draw an arc such that it cuts the bisector........
4. Do the same with point B and wherever those arcs meet name that point C.........

• Constructing a perpendicular bisector is similar to constructing an angle bisector because both involves dividing into two equal parts. ... However, when constructing a perpendicular bisector it is necessary to make the arc at both sides of the line.

[ Or ]

Let's assume side of equilateral triangle is 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.