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Angle sum property, Exterior angle property - Coggle Diagram
Angle sum property
proof
Proof for Angle Sum Property of a Triangle 
Since PQ is a straight line, it can be concluded that:
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Since PQ||BC and AB, AC are transversals,
Therefore, ∠QAC = ∠ACB (a pair of alternate angle)
Also, ∠PAB = ∠CBA (a pair of alternate angle)
Substituting the value of ∠QAC and∠PAB in equation (1),
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Thus, the sum of the interior angles of a triangle is 180°.
Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ←→ parallel to the side BC of the given triangle.
Interior angles of triangles measure 180° :
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Exterior angle property
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
proof
Consider a ∆ABC, as shown in the figure above. To prove the above property of triangles, draw a line PQ←→ parallel to the side BC of the given triangle.
Since PQ is a straight line, it can be concluded that:
-
Since PQ||BC and AB, AC are transversals,
Therefore, ∠QAC = ∠ACB (a pair of alternate angle)
Also, ∠PAB = ∠CBA (a pair of alternate angle)
Substituting the value of ∠QAC and∠PAB in equation (1),
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Thus, the sum of the interior angles of a triangle is 180°.
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