Question

construct and equilateral triangle given its side and justify the construction​

Answer 1

Answer:

11.1, 5 - Chapter 11 Class 9 Constructions. ... Let’s assume side of equilateral triangle is 5.5 cm In an equilateral triangle, all sides are equal So, our triangle looks like Let’s construct it Steps of construction 1. ... Thus, Δ ABC is the required equilateral triangle Justification ...

Answer 2

$\huge\star{\purple{\underline{\underline{\mathfrak{Explanation:}}}}}$

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$\bold{\red{Steps-of-construction:}}$

• Draw a line segment AB=4 cm .

• With A and B as centres, draw two arcs on the line segment AB and note the point as D and E.

• With D and E as centres, draw the arcs that cuts the previous arc respectively that forms an angle of 60° each.

• Now, draw the lines from A and B that are extended to meet each other at the point C.

• Therefore, ABC is the required triangle.

$\huge\star{\pink{\underline{\underline{\mathfrak{Justification:}}}}}$

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From construction, it is observed that

AB = 4 cm, ∠A = 60° and ∠B = 60°

We know that, the sum of the interior angles of a triangle is equal to 180°

∠A + ∠B + ∠C = 180°

SuBstitute the values

⇒ 60° + 60° + ∠C = 180°

⇒ 120° + ∠C = 180°

⇒ ∠C = 60°

While measuring the sides, we get

BC = CA = 4 cm (Sides opposite to equal angles are equal)

AB = BC = CA = 4 cm

∠A = ∠B = ∠C = 60°

$\large\star{\purple{\underline{\mathfrak{Hence,Justified!}}}}$