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Prove that all the angle of the triangle is 180

Posted by Dhairya Patel 8 years, 4 months ago

CBSE > Class 09 > Mathematics

1 answers

Krishna Maurya 8 years, 4 months ago

Construction : Through A, draw a line parallel to BC of ∆ ABC Proof: DE||BC and AB is transversal Angle ABC = Angle BAD ------------- (1) Angel ACB = Angel CAE ---------------(2) Add eq. (1) and (2) ABC + ACB = BAD +CAE Adding angel BAC both sides we get ABC+ ACB+BAC=BAD+CAE+BAC But, BAD + CAE+ BAC = DAE = 180° [ DAE is a straight angle] ABC +ACB+BAC = 180° Hence, the sum of the angles of a ∆ is 180°

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