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Asked by Sita Last Modified
Answer 
Tasneem
Let us draw an equilateral triangle of side 5 cm. We know that all sides of an equilateral triangle are equal. Therefore, all sides of the equilateral triangle will be 5 cm. We also know that each angle of an equilateral triangle is 60º.
The steps mentioned below will be followed to draw an equilateral triangle of 5 cm side.
Step I: Draw a line segment AB of 5 cm length. Draw an arc of some radius, while taking A as its centre. Let it intersect AB at P.
Step II: Taking P as centre, draw an arc to intersect the previous arc at E. Join AE.
Step III: Taking A as centre, draw an arc of 5 cm radius, which intersects extended line segment AE at C. Join AC and BC. ΔABC is the required equilateral triangle of side 5 cm.
Justification of Construction:
We can justify the construction by showing ABC as an equilateral triangle i.e., AB = BC = AC = 5 cm and ∠A = ∠B = ∠C = 60°.
In ΔABC, we have AC = AB = 5 cm and ∠A = 60°.
Since AC = AB,
∠B = ∠C (Angles opposite to equal sides of a triangle)
In ΔABC,
∠A + ∠B + ∠C = 180° (Angle sum property of a triangle)
⇒ 60° + ∠C + ∠C = 180°
⇒ 60° + 2 ∠C = 180°
⇒ 2 ∠C = 180° − 60° = 120°
⇒ ∠C = 60°
∴ ∠B = ∠C = 60°
We have, ∠A = ∠B = ∠C = 60° ... (1)
⇒ ∠A = ∠B and ∠A = ∠C
⇒ BC = AC and BC = AB (Sides opposite to equal angles of a triangle)
⇒ AB = BC = AC = 5 cm ... (2)
From equations (1) and (2), ΔABC is an equilateral triangle.
read less 
ABC is the required equilateral triangle of side 5 cm.
A = B = C = 60o.ABC, we have AC = AB = 5 cm and 
A = 60oB = C (angles opposite to equal sides of a triangle)ABC
A + B + C = 180o (angle sum property of a triangle)60o + C + C = 180o60o + 2 C = 180o 2 C = 180o - 60o = 120o C = 60o
A = B = C = 60o ... (1)A = B and A = CBC = AC and BC = AB (sides opposite to equal angles of a triangle)AB = BC = AC = 5 cm ... (2)ABC is an equilateral triangle.View 2 more Answers
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