The consecutive interior angles theorem states that the consecutive interior angles on the same side of a transversal line intersecting two parallel … Angle a is 145 deg and b is 35 deg, they equal 180. Consecutive Interior Angles (Example) Angles 3 and 5. consecutive interior angles alternate interior angles Use the figure in the Example for Exercises 1–12. 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. 5. Notes: Extra Practice In Exercises 1–4, find m∠1 and m∠2. 1.!9 and !13 2.!5 and !14 3.!4 and !6 Identify each pair of angles as alternate interior, alternate exterior, Examples In the diagram, ∠3and ∠5are supplementary, and ∠4 and∠6 are supplementary. Formally, consecutive interior angles may be defined as two interior angles lying on the … ⦣5 and ⦣7 are corresponding angles. Consecutive Interior Angles Converse : If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. 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. Consecutive interior angles are supplementary. 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. A. ... Identify an example of each type of angle pair. Theorem 3-12 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. So are angles 3 and 5. Name the transversal that forms each pair of angles. Corresponding angles ⦣1 and ⦣3 are corresponding angles. Two lines cut by a transversal line are parallel when the sum of the consecutive exterior angles is \$\boldsymbol{180^{\circ}}\$. Consecutive interior angles are consecutive angles sharing the same inner side along the line. Interior angles that are on the same side of the transversal. Theorem 3-11 If two different lines are parallel to a third line, then they are parallel to each other. Consecutive Interior Angles Theorem Consecutive Interior Angles (5 points) Statement Reason a and b are supplementary. Consecutive exterior angles are consecutive angles sharing the same outer side along the line. 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). Perpendicular Lines (Definition) Lines that intersect to form right angles.
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