Geom 1point4

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Geom 1point4

  1. 1. 1.4 Angles and Their Measures Objectives: - Use angle postulates - Classify angles as acute, right, obtuse, or straight
  2. 2. Angles <ul><li>An angle consists of two different rays that have the same initial point. </li></ul><ul><li>The rays are the sides of the angle. </li></ul><ul><li>The initial point is the vertex of the angle. </li></ul>A B C
  3. 3. Naming Angles <ul><li>Name the angles in the figure: </li></ul><ul><li>The measure of angle A is denoted by m _ A </li></ul><ul><li>The measure can be approximated with a protractor using units called degrees. (º) </li></ul>F G H I
  4. 4. Congruent <ul><li>Angles that have the same measure are called congruent angles . </li></ul><ul><li>Measures are equal, angles are congruent. </li></ul><ul><li>If angles BAC and DEF are both 50º, then the measure of the angles are equal, but the angles are congruent. </li></ul>
  5. 5. Protractor Postulate <ul><li>Look at the picture on the top of page 27. </li></ul><ul><li>Consider a point A on one side of line OB. The rays of the form Ray OA can be matched one to one with the real numbers for 0 to 180. </li></ul><ul><li>The measure of Angle AOB is equal to the absolute value of the difference between the real numbers for Ray OA and Ray OB. </li></ul>
  6. 6. Angle Terms <ul><li>A point is in the interior of an angle if it is between points that lie on each side of the angle. </li></ul><ul><li>A point is in the exterior of an angle if it is not on the angle or in its interior. </li></ul>
  7. 7. Angle Addition Postulate <ul><li>If P is in the interior of _ RST, then </li></ul><ul><ul><li>m _ RSP + m _ PST = m _ RST </li></ul></ul>
  8. 8. Example <ul><li>Look at the horse on the bottom of page 27 </li></ul><ul><li>Wearing blinkers, each eye can see 100º. The angle of vision that is seen by both eyes is 60º. Find the angle of vision seen by the left eye alone. </li></ul>
  9. 9. Classifying angles <ul><li>Acute angles measure less than 90º </li></ul><ul><li>Right angles measure 90º </li></ul><ul><li>Obtuse angles measure more than 90º </li></ul><ul><li>Straight angles measure 180º </li></ul>
  10. 10. Adjacent angles <ul><li>Two angles are adjacent angles if they share a common vertex and side, but have no common interior points </li></ul>
  11. 11. Do page 29, 1-22 together <ul><li>Homework: </li></ul><ul><ul><li>Worksheets </li></ul></ul>

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