Question

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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 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

Answer 1

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Explanation:

Statement Reason

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 Definition of corresponding angles in parallel lines

m∠1 = m∠4 and m∠3 = m∠5 Substitution of corresponding angles

m∠4 + m∠2 + m∠5 = 180° Angle addition and definition of a straight line

m∠1 + m∠2 + m∠3 = 180° Substitution.