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**Lesson 1**Transversals and Proportional Line Segments**Transversals**• Transversals-Lines that intersect two or more lines. • When a transversal cuts two parallel lines, four types of pairs of angles are formed.**Vertical angles pairs – angles across from each**other: 1&4, 3&2, 5&8, 7&6 Corresponding angle pairs – angles that correspond at each intersection: 2&6, 4&8, 1&5, 3&7 Alternate interior angle pairs – angles inside the parallel lines on alternate sides of the transversal: 3&6, 4&5 Alternate exterior angle pairs – angles outside the parallel lines on alternate sides of the transversal: 1&8, 2&7**If a transversal cuts two parallel lines, half the angles**formed are Obtuse angles that are all equal in measure, and the other half are Acute angles that are all equal in measure.**Proportional Segments**• Proportional segments – When two transversals cut three or more parallel lines, the resulting segments are proportional**2(SF) =**SF = 5 = x x = Toolbox 2) proportion and scale factor 5(SF) = x**(4z)°**(2y)° 3 4 140° x° 7 k Assignment: Problem Set 1 from the book with these changes: • 5. Find x, y, and z. 6. Solve for k. • 8. What are the measures of the two acute angles in an isosceles right triangle? • 12. Find the area of the figure in Problem 12 in Problem Set 1 in the book.