Lines and Angles

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# lines and angles - PowerPoint PPT Presentation

Lines and Angles . Geometry Chapter 3, Section 1. Notes . What does it mean for two lines to be parallel? Parallel lines: Lines that do not intersect and are coplanar . What about lines that don’t intersect and aren’t coplanar?

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### Lines and Angles

Geometry

Chapter 3, Section 1

Notes
• What does it mean for two lines to be parallel?
• Parallel lines: Lines that do not intersect and are coplanar.
• What about lines that don’t intersect and aren’t coplanar?
• Skew Lines: Lines that do not intersect and are not coplanar.
• What does it mean for two planes to be parallel?
• Parallel Planes:planes that do not intersect.
• Example: the planes containing the ceiling and floor are parallel
Notes
• Parallel Postulate:
• If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
• Parallel lines have the same slope (e.g. slope of 3 and 3)
• Tilted at the same angle
• Perpendicular Postulate:
• If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
• Perpendicular lines have slopes that are negative reciprocals (e.g. 4 and – 1/4)
• At 90 degrees from each other
Notes
• Transversal: a line that intersects two or

more lines in a plane at different points.

• E.g. Line c is a transversal to lines a and b.
• Line b is a transversal to which two other lines?
• a & c
• b & c
• When a transversal

intersects two lines,

how many angles are

formed?

• 8 angles are formed
Notes
• Angles formed by a transversal.
• We give certain pairs of these angles special names.
• Corresponding Angles: 1 & 5 ; 2 & 6 ; 3 & 7 ; 4 & 8
• Exterior Angles: 1, 2, 7, & 8
• Interior Angles: 3, 4, 5, 6
• Alternate Exterior Angles: 1 & 7 ; 2 & 8
• Alternate Interior Angles: 3 & 5 ; 4 & 6
• Consecutive Interior Angles: 4 & 5 ; 3 & 6
Notes
• Symbols for parallel in statements and figures
• The symbol ll means is parallel to
• The pink arrows on lines PQ and RS indicate that they are parallel.
Angle Pair Names Activity
• Using about ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
• Color the exterior angles all one color
• Color the interior angles all one color
• Label the exterior and interior angles
• Using another ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
• Color each pair of corresponding angles a different color.
• Label this quarter sheet of paper “corresponding angles.”
• Using another ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
• Color each pair of alternate exterior angles a different color.
• Color each pair of alternate interior angles a different color.
• Label this quarter sheet “alternate exterior and interior angles.”
• Using the final ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
• Color each pair of consecutive interior angles a different color.
• Label this quarter sheet “consecutive interior angles.