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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.