Consecutive Interior Angles

Consecutive Interior Angles Example:

∠3 and ∠6 are consecutive interior angles
∠4 and ∠5 are consecutive interior angles

Consecutive interior angles are supplementary
Consecutive interior angles add up to 180°

Given: a || b and t with transversal t
Prove: ∠3 and ∠6 are supplementary

Statement	Reason
a \|\| b and t with transversal t	Given
∠2 ≅ ∠6	Corresponding Angle Postulate
m∠2 ≅ m∠6	Definition of congruent angles
∠3 and ∠2 are supplementary	Linear pair postulate
m∠3 + m∠2 = 180°	Definition of supplementary angles
m∠3 + m∠6 = 180°	Substitution Property
∠3 and ∠6 are supplementary	Definition of supplementary angles

Shows you a proof of consecutive interior angles using parallel lines and a transversal

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consecutive interior angles: the pairs of angles that are between two lines and on the same side of the line cutting through the two lines.
interior angles: the angles between adjacent sides of a rectilinear figure
parallel lines: two lines which never cross and always the same distance apart
proof: an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion
supplementary angles: Two angles are supplementary angles if the sum of their measures is equal to 180°
transversal: a line that passes through two lines in the same plane at two distinct points.
two column proof: This consists of a list of statements, and the reasons that we know those statements are true. The two column proof has five parts:
1) Given
2) Proposition
3) Statement Column
4) Reason Column
5) Diagram