Prove that the sum of angles of a triangle is 180 °.
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Question:Prove that the sum of angles of a triangle is 180°
Given:
A ∆ABC
To prove:
<1+<2+<3=180°
Construction:
Through A, draw a line DAE||BC
Proof:
DAE||BC and AB is transversal
<4=<2 (Alternate int angle)
DAE||BC and AC is transversal
<5=<3 (Alternate int angle)
Now
DAE is a straight line
<4+<1+<5=180° (angle on the same side of DAE at the point A)
<1+<4+<5=180°
<1+<2+<3=180°. {<4=<2 and <5=<3}
Hence;The sum of the angles of a triangle is 180°