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Q.Prove the angle sum property.
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Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Proof:
Consider a ∆ABC, as shown in the figure( in the attachment) . 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:
∠PAB + ∠BAC + ∠QAC = 180° ………(1)
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),
∠ACB + ∠BAC + ∠CBA= 180°
Thus, the sum of the interior angles of a triangle is 180°.
Hence angle sum property of a triangle proved.
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![](https://hi-static.z-dn.net/files/d09/81103400893ae92e24dfa0736a0abe0e.jpg)
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Step-by-step explanation:
refer to the attachment
Attachments:
![](https://hi-static.z-dn.net/files/d6d/10967ce09473ddbf3d3b6ccb9e53da85.jpg)
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