Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.
Statement
Reason
Points A, B, and C form a triangle.
given
Let D⁢E― be a line passing through B and parallel to A⁢C― .
definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
Alternate Interior Angles TheoremAlternate Exterior Angles TheoremCorresponding Angles TheoremCongruent angles have equal measures.
m∠1 = m∠4 and m∠3 = m∠5
Alternate Interior Angles TheoremAlternate Exterior Angles TheoremCorresponding Angles TheoremCongruent angles have equal measures.
m∠4 + m∠2 + m∠5 = 180°
angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180°
substitution