plzzzzzzz... help......
Answers
ɢɪᴠᴇɴ :-
An equilateral triangle ∆ABC .
ᴛᴏ ᴘʀᴏᴠᴇ :-
An equilateral triangle is equiangular .
ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ:-
From vertex A drop a perpendicular on side BC . Mark it as point M .
From vertex A drop a perpendicular on side BC and mark it as point N .
ᴘʀᴏᴏғ :-
Firstly we know that in an equilateral triangle perpendicular bisector , altitude and median all concide with each other . Also they are equal for each of the vertices .
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Now we are required to Prove that ∠ A = ∠ B = ∠ C , that is all angles are equal and each equals to 60°.
So , by construction we can say that ∠ AMC = ∠BMC = 90° and AM = BM since CM is perpendicular bisector .
Therefore by corresponding parts of congruent triangles we can say that
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Similarly we can prove that ∆ BNA ∆ CNA .
Therefore by corresponding parts of congruent triangles we can say that
From all these we can conclude that
Answer:
AB=AC⇒∠C=∠B ......(1)since angles opposite to equal sides are equal.
Also,AC=BC⇒∠B=∠A .....(2) since angles opposite to equal sides are equal.
From (1) and (2) we have
∠A=∠B=∠C ...(3)
In △ABC,
∠A+∠B+∠C=180
∘
(Angle sum property)
⇒∠A+∠A+∠A=180
∘
⇒∠A=
3
180
∘
=60
∘
∴∠A=∠B=∠C=60
∘
Hence Proved.