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State and prove interior angle and theorem for triangleplease please answer me fast |
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Answer» Step-by-step explanation: 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. Proof for Angle SUM Property of a Triangle
Since PQ is a STRAIGHT line, it can be concluded that: ∠PAB + ∠BAC + ∠QAC = 180° ………(1) SincePQ||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°. |
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