Consecutive interior angles are consecutive angles sharing the same inner side along the line. Supplementary Angles (Definition) Angles that add to 180 degrees. Starting with the fact that angles 1 and a are a linear pair and that angles b and 2 are also a linear pair, use a two column proof to prove that consecutive interior angles a and b are supplementary. Corresponding angles ⦣1 and ⦣3 are corresponding angles. Theorem 3.4 Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. The diagram given below illustrates this. Perpendicular Lines (Definition) Lines that intersect to form right angles. Converse of the Consecutive Interior Angles Theorem If two lines are intersected by a transversal so that the consecutive interior angles are supplementary, then the lines are parallel. consecutive interior angles alternate interior angles Use the figure in the Example for Exercises 1–12. 5. 1.!9 and !13 2.!5 and !14 3.!4 and !6 Identify each pair of angles as alternate interior, alternate exterior, Two lines cut by a transversal line are parallel when the sum of the consecutive exterior angles is $\boldsymbol{180^{\circ}}$. ⦣5 and ⦣7 are corresponding angles. Examples In the diagram, ∠3and ∠5are supplementary, and ∠4 and∠6 are supplementary. Consecutive Interior Angles Theorem Consecutive Interior Angles Name the transversal that forms each pair of angles. Formally, consecutive interior angles may be defined as two interior angles lying on the … Same-side (consecutive) interior angles are non-adjacent angles that lie on the same side of the transversal (t) and between the lines (r and s). Section 3.1 (Special angles formed by parallel lines cut by a transversal.notebook 1 September 19, 2011 Objective: I can identify parallel lines, skew lines, transversals, alternate interior angles, alternate exterior angles, corresponding angles and consecutive interior angles. Theorem 3-12 Angle a is 145 deg and b is 35 deg, they equal 180. Consecutive interior angles are supplementary. Consecutive exterior angles are consecutive angles sharing the same outer side along the line. Consecutive Interior Angles Converse : If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. Consecutive Interior Angles (Example) Angles 3 and 5. Theorem 3-11 If two different lines are parallel to a third line, then they are parallel to each other. So are angles 3 and 5. Notes: Extra Practice In Exercises 1–4, find m∠1 and m∠2. (5 points) Statement Reason a and b are supplementary. A. Interior angles that are on the same side of the transversal. ... Identify an example of each type of angle pair. The consecutive interior angles theorem states that the consecutive interior angles on the same side of a transversal line intersecting two parallel …

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