Bowman’s Website

September 16, 2010

Geometry Notes — Lines, Coplanar Lines, and Angle Clusters

Filed under: Geometry, Geometry Notes — Tags: — bowman @ 10:22 am

Intersection – the set of points two figures have in common

If two lines intersect, their intersection is a single point.

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If two lines intersect, then they are either perpendicular or oblique.

Perpendicular lines – lines that intersect to form a right angle

Oblique lines – lines that intersect that are not perpendicular.

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If two lines do not intersect, then they are either parallel or skew.

Parallel lines – coplanar lines that do not intersect

Skew lines – non-coplanar lines that do not intersect

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Transversal – a line that intersects two or more coplanar lines at different points

Line t is a transversal. It intersects lines a and b at different points. The transversal creates two angle clusters.

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What kind of angles are 1 and 3? What kind of angles are 6 and 7?

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Interior versus Exterior angles…

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Alternate verses Same-side angles…

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Alternate interior angles – two non-adjacent interior angles on opposite sides of the transversal

3 and 5 are alternate interior angles. Which other pair of angles are alternate interior angles? 4 and 6

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5 and 6 are not alternate interior angles.  Why? They form a linear pair. They are adjacent.

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Alternate exterior angles – two non-adjacent exterior angles on opposite sides of the transversal

1 and 7 are alternate exterior angles. Which other pair of angles are alternate exterior angles? 2 and 8

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7 and 8 are not alternate exterior angles. Why? They form a linear pair. They are adjacent.

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Same-side interior angles – two non-adjacent interior angles on the same side of the transversal

4 and 5 are same side interior angles. Which other pair of angles are same side interior? 3 and 6

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Same-side exterior angles – two non-adjacent exterior angles on opposite sides of the transversal

Name 2 pairs of same-side exterior angles.1 and 8 are same side exterior angles. So are 2 and 7

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Corresponding angles – two non-adjacent angles on the same side of the transversal such that one angle is an interior angle and the other is an exterior angle.

1 and 5 are corresponding angles.  Notice how the two angles are in the same positions.  Both angles are in the top left position in each angle cluster.  Corresponding angles will have location in common.

Name 3 other pairs of corresponding angles. 2 and 6, 3 and 7, 4 and 8

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I just love geometry art. Lines, perpendicular lines, parallel lines, parallel powerpuff worlds. Outstanding.

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