Question

prove that sum of three angles of a triangle is 2 right angle​

Answer 1

$\huge{\rm{\red{Solution-}}}$

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Given :

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• ABC is a triangle, with three sides AB,BC and AC respectively and with three angles ∠ABC, ∠BCA, ∠BAC

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To prove :

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• Sum of angles of ∆ABC = 2 × 90° => 180°

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Construction :

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• Draw a line PQ through point A, which is parallel to BC

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Proof :

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∵ PQ is a straight line

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∴ $\angle{PAB}\:+\:\angle{BAC}\:+\:\angle{QAC}\:=\: 180^\circ$........(1)

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Also, PQ || BC

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∴ ∠QAC = ∠ACB and ∠PAB = ∠ABC (Alternate angles)

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Putting the values in (1)

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$\implies$ ∠ABC + ∠BCA + ∠BAC = 180°

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$\therefore$ Sum of angles of a triangle is twice of right angle.

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Hence proved!

Answer 2

$\huge \underline{ \rm \red{hello}}$

Question:-

prove that sum of three angles of a triangle is 2 right angle.

Solution:-

$\huge \sf\underline{ \rm {given}}$

ABC is a Triangle Whose Sides AB=AC

$\huge \sf\underline{ \rm {To \: Prove}}$

∠ ABC + ∠ACB + ∠BAC = 180° or 2× right angle.

$\huge \sf\underline{ \rm {construction}}$

Draw a line DE || BC from the vertex A.

$\huge \sf\underline{ \rm {proof}}$

∴ ∠ DAB = alternate ∠ABC ----- eq (1)

again,

DE || BC and AB bisects it.

∴ ∠EAC = Alternate ∠ACB ----- Eq. (2)

sum of both sides angle from equation ① and ②

∠DAB + ∠EAC = ∠ABC + ∠ACB

Now, adding both sides ∠BACB

∠DAB + ∠EAC ∠BAC = ∠ABC + ∠ACB+ ∠BAC

Even , if sum of the three angles is formed ∠DAE. ( according to linear angle)

∠DAE = ∠ABC +∠ACB +∠BAC

∴ ∠ABC + ∠ACB + ∠BAC = 180°

∴ ∠ABC + ∠ACB + ∠BAC = 2× right angles.

Hence , proved.