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16bf10lec6 - Math 16b Thomas Scanlon Autumn 2010 Thomas...

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Unformatted text preview: Math 16b Thomas Scanlon Autumn 2010 Thomas Scanlon Math 16b Angle measurements From geometry, we are used to measuring angles between two rays. Figure: ∠ BAC Thomas Scanlon Math 16b Straight angle If the rays are collinear but distinct, then we have a straight angle whose measure is by de nition 180 ◦ . Figure: m ∠ BAC = 180 ◦ Thomas Scanlon Math 16b Right angle If the rays are perpendicular, then we have a right angle which is half of a straight angle, and hence has a measure of 90 ◦ . Figure: m ∠ BAC = 90 ◦ Thomas Scanlon Math 16b Acute and obtuse angles An acute angle has a measure between 0 ◦ and 90 ◦ An obtuse angle has a measure between 90 ◦ and 180 ◦ . Figure: m ∠ BAC > 90 ◦ Thomas Scanlon Math 16b Zero degrees The angle between a ray and itself is ◦ . Figure: m ∠ BAC = ◦ Thomas Scanlon Math 16b Negative angles? If an angle of 0 ◦ is meaningful, what might we mean by an angle measure of less than zero? We will de ne the angle measurement from one ray to another (sharing a base point) in the counterclockwise direction to be positive and the angle measurement for the same rays but taken in the clockwise direction to be additive inverse of the rst measure....
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