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Angles and Parallel Lines: Types and Properties

Learn about the different types of angles formed when a transversal intersects parallel lines, including corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, consecutive exterior angles, vertical angles, and linear pairs.

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Angles and Parallel Lines: Types and Properties

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  1. Angles and Parallel Lines Unit 1

  2. Transversal • Definition: A line that intersects two or more lines in a plane at different points is called a transversal. • When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Consecutive exterior angles Alternate exterior angles Alternate interior angles Corresponding angles m t n

  3. Corresponding Angles Corresponding Angles: Two angles in the same position. These angles are congruent. 1 2 3 4 5 6 7 8

  4. Alternate Interior Angles • Alternate Interior Angles: Two angles that are on opposite sides of the transversal and inside the parallel lines. These angles are congruent. Circle 4 and 5 as an example of this type. 1 2 3 4 5 6 7 8

  5. Alternate Exterior Angles • Alternate Exterior Angles: Two angles that are on opposite sides of the transversal and outside the parallel lines. The angles are congruent. 1 2 3 4 5 6 7 8

  6. Consecutive Interior Angles Consecutive Interior Angles: Two angles on the same side of the transversal and inside the parallel lines. These angles are supplementary (=180°). 1 2 3 4 5 6 7 8

  7. Consecutive Exterior Angles • Consecutive Exterior Angles: Two angles on the same side of the transversal and outside the parallel lines. These angles are supplementary (= 180°). 1 2 3 4 5 6 7 8

  8. Vertical Angles Two angles that are across from each other. These angles are congruent. Vertical Angles: 1 2 3 4 5 6 7 8

  9. Linear Pair • Linear Pair: Supplementary angles that form a line (sum = 180) 1 2 3 4 5 6 7 8

  10. Angles and Parallel Lines • If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. • Corresponding angles • Alternate interior angles • Alternate exterior angles • If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. • Consecutive interior angles • Consecutive exterior angles • Linear Pair

  11. B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example:If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80°

  12. B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example: If line AB is parallel to line CD and s is parallel to t, find: 1. the value of x, if m<3 = 4x + 6 and the m<11 = 126. 2. the value of x, if m<1 = 100 and m<8 = 2x + 10. 3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. ANSWERS: 1. 30 2. 35 3. 33

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