Prove that “The sum of the angles in a triangle is 180“.

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!

Best regards!!

you cant answer this dummy

step-by-step explanation:

do you have a picture of the table