Download Chapter One Learning Goals

An Informal Introduction to Geometry
This illustration shows how to construct a regular pentagon with given side ab. Try it!
Chapter One Learning Goals
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Develop clear language to describe shapes.
Write and follow careful directions.
Use hand construction tools.*
Use a protractor to measure angles
Know the invariant property of points on a perpendicular bisector of a line
segment
Know the properties of the special segments assosciated with triangles: median,
altitude, angle bisector, and perpendicular bisector. Know their points of concurrency.
Indentify invariants-values or relationships that stay the same while other values or relationships change.
Use geometry software to construct “unmessupable” figures from their required characteristics.**
Use geometry software to measure and investigate geometric figures and to discover invariant properties of classes of
figures.
Identify the essential properties of rectangles, squares, parallelograms, equilateral triangles, and rhombuses.
Search for invariant numbers such as constant sums, products, ratios.
Search for spatial invariants such as concurrency, collinearity, perpendicularism, and parallelism.
Identify the invariant relationships for the sum of the measures of the angles in polygons.
Identify the invariant relationship that exists when a line parallel to tone side of a triangle cuts the other two sides
proportionally.
Use geometry software to tinker with geometric models.
*Basic Compass and straightedge constructions to Know: (There are
videos of these on my web page.)
Construct a triangle given three side lengths
Construct an angle congruent to a given angle
Constructing a perpendicular bisector of a line segment.
Construct the bisector of a given angle
Construct a perpendicular to a given line, both from a point ON the line and
from a point OUTSIDE the line.
**Geometer Sketchpad constructions to know. ( All un-
messupable.) (There is a link to sketchpad help on the web site.)
Square
Rhombus
Circle with radius the same as a given line segment.
Equilateral triangle
Isosceles triangle/ isosceles right triangle
Rectangle
Parallelogram
Regular polygon with given number of sides(using rotation menu)
Altitudes/angle bisectors/medians/perpendicular bisectors of a triangle.
Know how to measure angle, lengths, perimeters, areas, ratios,
Know how to make and use a table.
Additional Vocabulary: centroid, orthocenter, circumcenter, incenter, distance from a point to a line, legs/base of
isosceles triangle, skew lines