 Defining and Measuring Geometric Attributes Math Alliance September 28, 2010 Kevin McLeod Chris Guthrie

Geometry in the Real World Turn and talk to a shoulder partner: What examples of the following geometric ideas have you encountered in real life over the last week?  Triangles  Symmetry  Regular patterns (tesselations)

Geometric Definitions Discuss at your table: How would you define the following geometric terms?  Point  Line  Plane Find examples of each one in this room.

Euclid’s Definitions (Don’t Try These at Home!)  A point is that which has no part  A line is breadthless length  A straight line is a line which lies evenly with the points on itself  A surface is that which has length and breadth only  A plane surface is that which lies evenly with the straight lines on itself

Measuring Length  Measure some object in the room (perhaps your left index finger) to the nearest inch  Report your measurement, to the nearest inch, remember, to your shoulder partner, and receive a similar measurement in return.  Using only the measurement that was reported to you, what can you say about the true length of the object your partner measured?

Measuring Length (Contd.)  Measure some other object in the room to the nearest half inch  Report your measurement to your shoulder partner, and receive a similar measurement in return.  Using only the measurement that was reported to you, what can you say about the true length of the object your partner measured?

The Process of Measurement  Decide on the attribute to be measured  Select a unit that has that attribute  Fill, cover or match the unit to the attribute of the object

How Long Is This Crayon?

Segments, Rays and Angles  Segment AB is the set of points A and B and all the points on line AB which lie between A and B  Ray AB is set of points consisting of A and all points on line AB which lie on the same side of A as point B  Angle  ABC is the union of two noncollinear rays BA and BC that have a common endpoint (B). B is called the vertex of the angle

Measuring Angles  Use a protractor to measure the interior of the angle in Figure 10.8 (page 569) to the nearest degree  Using only the reported measurement to the nearest degree, what can you say about the true measure of the angle?

Measuring Angles  Which of these angles is larger?