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PROPERTIES OF PARALLEL LINES

PROPERTIES OF PARALLEL LINES. Transversal Line that intersect two coplanar lines at two distinct points Eight angles are formed by a transversal line. 5. 6. 1. 3. 4. 2. 7. 8. Alternate interior angles Angles inside the two lines on opposite sides of the transversal <3 and < 4

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PROPERTIES OF PARALLEL LINES

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  1. PROPERTIES OF PARALLEL LINES

  2. Transversal Line that intersect two coplanar lines at two distinct points Eight angles are formed by a transversal line 5 6 1 3 4 2 7 8

  3. Alternate interior angles Angles inside the two lines on opposite sides of the transversal <3 and < 4 <1 and <2 1 3 4 2

  4. Same side interior angles Angles inside the two lines on the same side of the transversal < 1 and < 4 < 2 and < 3 1 3 4 2

  5. Corresponding angles Angles that are in similar positions on the same side of a transversal <2 and <6 <5 and < 4 <1 and <7 <3 and <8 5 6 1 3 4 2 7 8

  6. When a transversal intersect two PARALLEL lines, then corresponding angles are congruent in other words they have the same angle measure The two small red arrows indicate the two lines are parallel 5 6 1 3 4 2 7 8

  7. When a transversal intersect two PARALLEL lines the alternate interior angles are congruent In this example < 1 and < 2 <3 and < 4 1 3 4 2

  8. When a transversal intersects two PARALLEL lines, then the same-side interior angles are supplementary This is saying m < 1 + m < 4 = 180 Likewise m < 2 + m < 3 = 180 1 3 4 2

  9. What are some things we can state from this diagram? Parallel lines Alternate interior angles Corresponding angles Same side interior angles Vertical angles If <6 and < 2 are corresponding then <1 and <6 are vertical so <1 and < 2 would also have the same measure 5 6 l 1 3 4 2 m 7 8 t

  10. Find the measure of each angle: c d 8 7 6 a 2 500 4 5 b 1 3

  11. Find the values of x and y x = Corresponding angles of parallel lines are congruent y = 70 + 50 + y = 180 500 x y 700

  12. Find the values of x and y. Then find the measure of the angles Same side interior angles = 180 90 + 2x = 180 x = 45 y + y – 50 = 180 2y – 50 = 180 2y = 230 y = 115 115 90 y 2x 65 (y – 500) 90

  13. ASSIGNMENT Page 118 1 – 8 11 - 25

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