Question

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

Answer 1

Answer:

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.

$\angle ABC+\angle BAC+\angle ACB=180\°$

Proof:

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

∴ $\angle PAB+\angle BAC+\angle QAC=180\°$ ....Angle Addition Postulate...........( 1 )

PQ || BC

$\angle PAB=\angle ABC$ .....Alternate Angle Postulate as PQ || BC...( 2 )

Similarly,

$\angle QAC=\angle ACB$ .....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 )

$\angle ABC+\angle BAC+\angle ACB=180\°$ ...Proved

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