Download 9/29/13 1 Building Blocks of Geometry Two Ways to Define Angles

9/29/13 Building Blocks of Geometry
  Identify: •  point •  line •  line segment •  ray •  angle •  vertex 1 Two Ways to Define Angles
  There are two ways to think about angles. •  as the result of two rays, lines, or segments meeting at a common point Static view (angles in a drawn figure) •  as a measure of the smallest counterclockwise turn between two rays, lines, or segments that meet at a common point Dynamic view (angle as a turn) 2 1 9/29/13 Angle Misconceptions
  Children often confuse angle measure with length measure, and judge the size of an angle by the lengths of its sides instead of the size of the turn. Angle a Angle b In fact, angle B is larger than angle A because the the size of the turn in angle B is greater than the size of the turn in angle A. “Angle A is larger than angle B because angle A has longer sides than angle B.” 3 Benchmark Angles
A right angle measures 90°.
A straight angle measures 180°.
One complete turn is 360°.
  We can use these benchmark angles to determine the measure of the interior angles of the different pattern blocks. Orange square Green triangle Red trapezoid Blue rhombus Yellow hexagon Tan rhombus 4 2 9/29/13 Determining Pattern Block Angles
Key idea:   Angle measure is additive. When an angle is decomposed into non-­‐overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. When 3 hexagons are placed together at a point, three of the angles make a circle. What is the measure of each angle? The smaller angles of 3 tan rhombuses cover one angle of the square. What is the measure of the smaller angle in the tan rhombus? 5 Measuring Angles
  A complete turn forms a circle and measures 360°.
360°
  A one-­‐degree angle turns 1/360 of a circle, and an angle that turns through n one-­‐degree angles has a measure of n degrees.
A 21° angle turns through 21 one-­‐degree angles. 21°
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