Informal Geometry
Edition: 2
Copyright: 2017
Pages: 192
Edition: 2
Copyright: 2017
Pages: 192
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Informal Geometry supports learning geometry through exploration, patterns, and conjecture. Topics include measurement, symmetry, isometries, and proportions, with scaling as a major theme.
Concepts are explained with clearly drawn illustrations, and at the end of each section is a set of “Understanding the Text” questions to help the reader focus on the main ideas. The exploratory nature of this text makes it useful for supporting future educators’ work in mathematical practices as well as supporting students studying the visual arts.
1 Points, Lines, and Planes
1.1 Points
1.2 Lines, Rays, and Line Segments
1.3 Planes
1.4 Collinear and Coplanar Points
1.5 Intersections of Parallel Lines and Planes
2 Rays and Angles
2.1 Definitions, Notation, and Measurement
2.2 Special Pairs of Angles
3 Triangles
3.1 Triangles and Their Special Angles
3.2 Special Angle Measure of Equilateral Triangles
3.3 Median, Altitude, and Angle Bisectors
4 Quadrilaterals and Special Angles
4.1 Quadrilaterals
4.2 Special Angles of Quadrilaterals
5 Polygons and Special Angles
5.1 Polygons
5.2 Special Angles of Polygons
6 Symmetry and Isometry in Two-Dimensions
6.1 Symmetry of Polygons and Other Figures
6.2 Symmetry Groups
6.3 Tessellations
6.4 Isometry Movements
6.5 Composition of Isometry Movements
6.6 Symmetry of Tessellations
7 Symmetry in Three Dimensions
7.1 Polyhedra
7.2 Symmetry of Polyhedra
8 Measurement
8.1 Introduction to Measurement
8.2 Length
8.2.1 Linear Measurement and Unit Conversions
8.2.2 Perimeter and Circumference
8.3 Area
8.3.1 Finding Area
8.3.2 Area Unit Conversions
8.3.3 Surface Area
8.4 Volume
8.4.1 Finding Volume
8.4.2 Volume Unit Conversions
8.5 Weight
8.6 Other Measurements
8.7 The Pythagorean Theorem
9 Scaling
9.1 Scaling Objects on the Plane
9.2 Scale Models
10 Proportions and Geometric Sequences
10.1 Proportions
10.2 Geometric Sequences
A Constructions
A.1 Constructing a Line Parallel to Another Line Through a Given Point
A.2 Constructing a Line Perpendicular to a Given Line
A.3 Constructing a Line Perpendicular to a Given Line Through a Given Point
A.4 Bisecting an Angle
A.5 Constructing an Equilateral Triangle