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GEOMETRY NOTES Lesson 3.1 Line Pairs and Transversals Rode2010 Key words: skew lines, transversal, corresponding angles, alternate interior angles, alternate interior angles. Review for the Lesson Adjacent angles share a common vertex and side. What does adjacent mean? Two angles are _____________________ angles if the sum of their measures is 180o. Sketch a diagram for each statement: Draw ∠ࡽࡾࡼ. Identify the vertex in your drawing. Lines m and n intersect at point P What is a plane? Is it a defined or undefined term? Lesson 3.1 Two lines that lie in the same plane are considered coplanar. l line l and line p are coplanar p Two lines that lie in different planes are considered noncoplanar and are called skew lines. n line m and line n are skew lines m Throughout this class we will assume that all lines are coplanar unless otherwise stated. Page 1 When a pair of lines is drawn, two distinct regions are formed: The interior region lies between the two lines. The exterior region is the area remaining outside the lines. A line that intersects two or more lines in different points is called a transversal. w p Line w intersects line p and line q. Line w is a transversal. q When two lines are intersected by a transversal four different types of angle pairs are formed. 1 2 3 4 5 6 7 8 Type of angle pair Definition Alternate Interior Angles Angles are interior angles Angles are on opposite sides of the transversal Angles do not have the same vertex Corresponding Angles One angle is an interior angle, the other is an exterior angle Angles are on the same side of the transversal Angles do not have the same vertex Alternate Exterior Angles Angles are exterior angles Angles are on the opposite sides of the transversal Angles do not have the same vertex Examples Trick to Identify Angle Pairs: Alternative interior angles form a “Z” shape and corresponding angles form a “F” shape. You may have to rotate the paper to see the “Z” or the “F”. Page 2