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Informal Geometry and Measurement Concepts

Learn about undefined terms, measuring angles and lines, relationships, circles, and constructions using basic tools in informal geometry.

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Informal Geometry and Measurement Concepts

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  1. 1.2 Informal Geometry and Measurement • Undefined terms (terms that are described not defined) • Point: • Represented by a dot • Has location, not size • Has no dimension • Line • Infinite set of points • Have a quality of “straightness” • One-dimensional • Represented symbolically by  (Fig 1.9 p. 10) • Collinear: 3 points on the same line __ • Line segment: part of a line between two points: BC • Midpoint: a point equal distance from the ends of a line segment • Plane • Two-dimensional • Infinite number of points and infinite number of lines • Coplanar points: lie in the same plane.

  2. Measuring line segments • Line segment is part of a line consisting of 2 distinct points. • We label a line or line segment by its endpoints. • Fig 1.11 & 1.9 p. 11 • Tool: Ruler • Metric conversion: 1 inch = 2.54 cm

  3. Measuring angles • Tool: Protractor • Angle’s size depends on the amount of opening between its sides. • Unit of measure: degree • Naming Angles: (Fig 1.10 p. 11) • Where the two sides meet is the vertex. • The vertex is always in the middle with the point on each side surrounding it. ABC . • Ex 4 – 5 p. 14-15

  4. Relationships • Parallel lines, never meet. Figure 1.19 p. 14 • Congruent angles have angles of equal measure. • Bisect an angle means to cut the angle in half. • Straight angle has 180 and is a straight line. • Intersecting lines have a point in common. • Perpendicular lines intercept to form two congruent angles. Each is 90. • Right angles are 90.

  5. CirclesFig 1.25 p. 15 • Set of all points in a plane that are at a given distance from a particular point (center) • Arc is any part of the circle between any of its two points. • Radius is any line segment joining the center to a point on the circle. We use a Compass (fig. 1.24) to draw circles or parts of circles (arcs)

  6. Constructions • Tools: • Compass • Straight edge. • Constructions: use ONLY these two tools: • Construct a segment congruent to a given line segment AB. P. 16, Fig. 1.26 • Construct the midpoint M of a given line segment AB. • P. 16, Fig 1.27

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