Answer
See below :)
Step-by-step explanation:
Experimental Verification
Step 1 : Three triangles with different shapes and sizes are drawn. Suppose the name of each triangle is ABC.
( Draw the triangles in such a way that you can each angle by using a protractor )
( See attached picture )
Step 2 : Measure each angle of these three triangles with the help of protractor and fill up the following table.
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Figure < A < B < C < A + <B + <C Result
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( i ) 180°
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( ii ) 180°
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(iii) 180°
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Conclusion : The sum of the angles of any triangle is equal to 180°
Theoretical proof
( See attached picture )
Given : <ABC , <BCA and <BAC are the angles of ∆ABC.
To prove : <ABC + <BCA + <BAC = 180°
Construction : Through the vertex A , a straight line XY parallel to BC is drawn.
Proof :
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Statements Reasons
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1. < XAB = <ABC 1. XY // BC and alternate
angles
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2. <YAC = <BCA 2. XY//BC and alternate
angles
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3. <XAB + <BAC + 3. whole part axiom
<YAC = <XAY
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4. <XAB + <BAC + 4. < XAY is a straight angle.
<YAC = 180°
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5. <ABC + <BAC + 5. from statements ( 1 ),
<BCA = 180° ( 2 ) and (4)
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Proved
Hope I helped!
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