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1 G.2a Angles and Parallel Lines

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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: Linear Pair & Vertical Angles still apply! +Corresponding Angles Alternate Angles Consecutive Angles t m n

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3 Vertical Angles & Linear Pair Vertical Angles: Linear Pair: 1 4, 2 3, 5 8, 6 7 Two angles that are opposite angles. Vertical angles are congruent. 1 & 2, 2 & 4, 4 & 3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5 Supplementary angles that form a line (sum = 180 )

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4 Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. 1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. 1. Consecutive interior angles 2. Consecutive exterior angles Continued…..

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5 Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions. 2 6, 1 5, 3 7, 4

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6 Alternate Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 3 6, 4 5 2 7, 1

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7 Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m 3 +m 5 = 180º, m 4 +m 6 = 180º m 1 +m 7 = 180º, m 2 +m 8 = 180º

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8 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 ° t s D C B A

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

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