# Construct the following and give justification :An equilateral triangle if its altitude is 3.2 cm.

Given : An equilateral triangle with Altitude : 3.2 cm

Steps of Construction :

1.         Draw a line XY and take a point D on it .

2.         Draw line DE with $90^{\circ}$ angle at D.

3.         Cut the line DE with arc of radius 3.2 cm at point A

4.         Make an angle of $30^{\circ}$ at A which cuts XY at B.

5.         Now find the length of BD and as center D cut the line XY at point C with radius equal to BD.

6.         Join AC

ABC is the required triangle.

Justification :

Here $\angle A = \angle BAD + \angle CAD$

$=30^{\circ}+30^{\circ}=60^{\circ}$

$AD\perp XY$

In DABD,$\angle BAD + \angle DBA + \angle ADB = 30^{\circ}+60^{\circ}+90^{\circ}=180^{\circ}$

$\angle A = \angle B = \angle C = 60^{\circ}$

Hence it is an equilateral triangle.

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