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## PowerPoint Slideshow about 'lines and angles' - lotus

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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
- How about line a?
- 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.

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