Question

show that the angles of an
equilateral triangle are 60degree each​

Answer 1

TO PROVE :-

• The measure of each angle in an equilateral triangle is 60°

SOLUTION :-

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Since the given triangle is equilateral . All sides are equal

$\implies \sf \: AB = AC = BC$

The angles opposite to equal sides are also equal ,

$\implies \sf \angle A = \angle B = \angle C$

Now ,

$\large {\underline {\boxed {\sf{ \red{sum \: of \: all \: angles \: in \: a \: triangle \: = 180 {}^{0} }}}}}$

$\implies \sf \: \angle A + \angle B + \angle C = 180 {}^{0} \\ \\ \implies \sf \: 3( \angle A ) = 180 {}^{0} \\ \\ \implies \sf \: \angle A = \frac{180}{3} \\ \\ \implies {\underline {\boxed {\pink{\sf {\: \angle A = 60 {}^{0} }}}}}$

$\implies {\underline {\boxed {\blue{ \sf {\: \angle A = \angle B = \angle C = 60 {}^{0} }}}}}$

$\huge {\underline{\blue{\boxed {\green{\mathbf{HENCE\:PROVED}}}}}}$

ADDITIONAL INFO :-

◉ Perimeter of an equilateral triangle = 3a

Where ,

• a is side of the equilateral triangle

◉ Area of equilateral triangle is given by ,

$\large {\underline {\boxed {\sf{a = \frac{ \sqrt{3} }{4} {a}^{2} }}}}$

◉ If in a given triangle two sides are equal , then the triangle is said to be isosceles triangle

◉ If in a given triangle No sides are equal then the triangle is said to be scalene triangle

Answer 2

TO PROVE :-

The measure of each angle in an equilateral triangle is 60°

SOLUTION :-

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Since the given triangle is equilateral . All sides are equal

\implies \sf \: AB = AC = BC⟹AB=AC=BC

The angles opposite to equal sides are also equal ,

\implies \sf \angle A = \angle B = \angle C⟹∠A=∠B=∠C

Now ,

\large {\underline {\boxed {\sf{ \red{sum \: of \: all \: angles \: in \: a \: triangle \: = 180 {}^{0} }}}}}

sumofallanglesinatriangle=180

0

\begin{gathered} \implies \sf \: \angle A + \angle B + \angle C = 180 {}^{0} \\ \\ \implies \sf \: 3( \angle A ) = 180 {}^{0} \\ \\ \implies \sf \: \angle A = \frac{180}{3} \\ \\ \implies {\underline {\boxed {\pink{\sf {\: \angle A = 60 {}^{0} }}}}}\end{gathered}

⟹∠A+∠B+∠C=180

0

⟹3(∠A)=180

0

⟹∠A=

3

180

⟹

∠A=60

0

\implies {\underline {\boxed {\blue{ \sf {\: \angle A = \angle B = \angle C = 60 {}^{0} }}}}}⟹

∠A=∠B=∠C=60

0

\huge {\underline{\blue{\boxed {\green{\mathbf{HENCE\:PROVED}}}}}}

HENCEPROVED

ADDITIONAL INFO :-

◉ Perimeter of an equilateral triangle = 3a

Where ,

a is side of the equilateral triangle

◉ Area of equilateral triangle is given by ,

\large {\underline {\boxed {\sf{a = \frac{ \sqrt{3} }{4} {a}^{2} }}}}

a=

4

3

a

2

◉ If in a given triangle two sides are equal , then the triangle is said to be isosceles triangle

◉ If in a given triangle No sides are equal then the triangle is said to be scalene triangle