The sum of the interior angle measures of abc is 180 proof

The Proof for, The sum of the interior angle measures of ΔABC is 180° is below.

Step-by-step explanation:

Given:

Draw a ΔABC ,

Construction:

Draw PQ Parallel to Side of triangle BC,

PQ || BC

To Prove:

The sum of the interior angle measures of ABC is 180.

Proof:

P - A - Q is a Straight Line, m∠PAQ = 180°      ...... Straight Angle

∴ ....Angle Addition Postulate...........( 1 )

PQ || BC

.....Alternate Angle Postulate as PQ || BC...( 2 )

Similarly,

.....Alternate Angle Postulate as PQ || BC...( 3 )

Now by Substituting ∠PAB and ∠QAC in  ( 1 ) and ,Transitive Property we get From ( 1 ) , ( 2 ) and ( 3 )

...Proved

i.e The sum of the interior angle measures of Δ ABC is 180°

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