3.1 Parallel Lines and Transversals

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Presentation transcript:

3.1 Parallel Lines and Transversals Comp book 3.1 Parallel Lines and Transversals Essential Question: How do we use parallel lines and transversals to identify angle measures? Take out 4 different colored pencils from blue box…or your own

Complementary Angles = When sum of two angles equals 90° Comp book Complementary Angles = When sum of two angles equals 90° O R N E

Supplementary Angles = Straight When sum of two angles equals 180° Comp book Supplementary Angles = Straight When sum of two angles equals 180°

Vocabulary P || Q L ⊥ M Comp book Parallel Lines – Lines in the same plane that do not intersect Perpendicular Lines – Intersecting lines whose angle measures 90° P || Q The symbol || means “is parallel to.” L ⊥ M The symbol ⊥ means “is perpendicular to.”

Comp book Transversal: a line that intersects two or more lines. Transversals to parallel lines form special angle pairs. A ll B A B

Adjacent angles: (next door & supplementary = 180) Foldable Adjacent angles: (next door & supplementary = 180) 1 & 2 2 & 3 4 3 1 2 5 6 8 7 3 & 4 4 & 1 5 & 6 5 & 8 6 & 7 New diagram: color 7 & 8

Vertical angles: (opposite & congruent) Foldable 1  3 2  4 4 3 1 2 5 6 8 7 5  7 6  8 New diagram: color

Corresponding angles: f d Corresponding angles: a b c

Foldable

If parallel lines are crossed by a transversal then corresponding angles are congruent *because lines are parallel* Not Corresponding: because lines are not parallel* 5 2 3 8 7 4 1 6 4 3 2 1 6 5 8 7

Foldable Interior angles: New diagram: Discuss the meaning of interior: color angles

Foldable

Foldable Exterior angles: New diagram: color exterior angles

Foldable

Foldable

Foldable Adjacent Vertical

Subtract known angle (100 degrees) from 180 degrees to find its supplementary adjacent angle 80

80 and 100 form supplementary angle 80 100

Vertical angles are congruent 80 100 80

Corresponding angles from one of the parallel lines are all congruent to their corresponding angles on the second parallel line 80 100 100 80 100 80 80

Find missing variable (x + 12)0 660

Find missing variable 120 (x + 50)

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