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Geometry Basics and Angle Measurements

Learn about angles, rays, vertex, degrees, angle addition postulate, classification of angles, and more in this comprehensive lesson. Includes examples and exercises.

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Geometry Basics and Angle Measurements

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  1. V T Y X U W Bell Work Given the coordinates of one endpoint of AB and its midpoint M, find the coordinates of the other endpoint. 1. A(0, 9); M(2, 5) 2. B(-5, 1); M(1, -1) In the figure at the right, WY bisects UV at Y and UY bisects TW at X. For each situation, find the value of x and the measure of the indicated segment. 3. UY = 4x – 3 and YV = x, find UV 4. UV = x + 6 and UY = x – 1, find YV

  2. Go over Rest of HW

  3. Vocabulary • Go through Pg. 44 – 48 and define the following terms: • Angle • Ray • Opposite rays • Sides • Vertex • Interior • Exterior • Degrees • Measure • Right Angle • Obtuse Angle • Acute Angle • Congruent Angles • Angle bisector

  4. What is an angle? • An angle is defined in terms of the two rays that form the angle. • A ray extends indefinitely in one direction. • Opposite rays make a line. • An angle is a figure formed by two noncollinear rays with a common endpoint.

  5. Parts of the angle • The two rays of the angle are called the sides. • The common endpoint of the angle is called the vertex. Interior exterior

  6. Measuring Angles • Angles are measured in units called degrees. • They can be measured by using a protractor.

  7. Angle Addition Postulate • If R is in the interior of <PQS, then m<PQR + m<RQS = m<PQS. If m<PQR + m<RQS = m<PQS, then R is in the interior of <PQS.

  8. Classifying Angles • A right angle measures 90 degrees. • An obtuse angle measures greater than 90 degrees. • An acute angle measures less than 90 degrees. • Congruent angles have the same measure.

  9. Angle Bisector • An angle bisector divides an angle in two congruent angles.

  10. Check Your Understanding • Pg. 49 # 3 – 16

  11. Homework • Pg. 50 # 17 – 39

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