prove that the sum of a Δ is 180 deg.
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See diagram.
Draw ABC as any triangle.
Now, draw a straight line parallel to BC through A.
Now angle DAG = angle BAC - opposite angles at an intersection of two lines.
Angle DAE = angle ABC as they are angles formed by a line AB intersecting
two parallel lines - included angle.
Angle GAF = angle EAC - opposite angles at intersection of two lines at A
Angle GAF = angle BAC as BC and FE are parallel. AC is intersecting both
lines. These are included angles.
Sum of these angles at A = angles DAG + GAF + EAD = 180 degrees.
At any point the total angle 360° degrees is divided into 180° and 180° by a
straight line.
So sum of angles A+B+C = 180° degrees
Draw ABC as any triangle.
Now, draw a straight line parallel to BC through A.
Now angle DAG = angle BAC - opposite angles at an intersection of two lines.
Angle DAE = angle ABC as they are angles formed by a line AB intersecting
two parallel lines - included angle.
Angle GAF = angle EAC - opposite angles at intersection of two lines at A
Angle GAF = angle BAC as BC and FE are parallel. AC is intersecting both
lines. These are included angles.
Sum of these angles at A = angles DAG + GAF + EAD = 180 degrees.
At any point the total angle 360° degrees is divided into 180° and 180° by a
straight line.
So sum of angles A+B+C = 180° degrees
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