Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.

Question

Reset NextStatementReason
Points A, B, and C form a triangle.	given
Let  be a line passing through B and parallel to .	definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
m∠1 = m∠4 and m∠3 = m∠5
m∠4 + m∠2 + m∠5 = 180°	angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180°	substitution

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Answer 1

No diagram is attached. So for this to work angle 1 is at A, angle 2 is at B and angle 3 is at C. In addition, angle 4 is the alternate interior angle to angle 1 once DE is constructed, as is angle 5 to angle 3.

Then the missing reasons are alternate interior angles theorem and definition of congruent angles