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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

• 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

• 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

• 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

• 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

• 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.

• 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.