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1 G.2a Angles and Parallel Lines. 2 Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal.

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Presentation on theme: "1 G.2a Angles and Parallel Lines. 2 Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal."— Presentation transcript:

1 1 G.2a Angles and Parallel Lines

2 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

3 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  )

4 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…..

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

6 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  

7 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

8 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

9 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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