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Standards of Learning--Geometry Resources

There are links at the bottom of this page and every page on GeoLibrary to link to other GeoLibrary pages. This course is designed for students who have successfully completed the standards for Algebra I. The course, among other things, includes the deductive axiomatic method of proof to justify theorems and to tell whether conclusions are valid. Methods of justification will include paragraph proofs, flow charts, two-column proofs, indirect proofs, coordinate proofs, and verbal arguments. A gradual development of formal proof is encouraged. Inductive and intuitive approaches also should be used.

This set of standards includes emphasis on two- and three-dimensional reasoning skills, coordinate and transformational geometry, and the use of geometric models to solve problems. A variety of applications and some general problem-solving techniques should be used to implement these standards, including algebraic skills. Calculators, computers, and graphing utilities (graphing calculators or computer graphing simulators) should be used by the student where feasible. Any technology that will enhance student learning should be used.

Geometry Glossary
Definitions for Geometry
Geometry - Math for Morons Like Us
The Basic Postulates and Theorems of Geometry
Geometry Theorems: Measure
Basic Math FAQ
Geometry Online's Logic Page
Geometry in Motion

G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include

identifying the converse, inverse, and contrapositive of a conditional statement; Page 3 -- Truth Tables
Page 4 -- Conditionals
Contrapositive, Converse and Inverse
translating a short verbal argument into symbolic form; Logic
diagramming arguments involving quantifiers (all, no, none, some), using Venn diagrams; and
using valid forms of deductive reasoning, including the law of syllogism.

Rules of Reasoning
Section 1.1 Review -- Logical Forms and Equivalences

G.2 The student will use pictorial representations, including computer software and coordinate methods to solve problems involving symmetry and transformation. This will include

using formulas for finding distance, midpoint, and slope; [Slope and Y-Intercept of a Straight Line] ctoy\MAT120\Topics in HTML\topic 09
Math Forum - Ask Dr. Math -- When is a slope 0 or undefined?
2.2 Slope

Math Review - Geometry
investigating and determining whether a figure is symmetric with respect to a line or a point; and

Symmetry and Pattern: The Art of Oriental Carpets
determining whether a figure has been translated, reflected, or rotated.

Types of Symmetry in the Plane
Wallpaper Groups
Computer Art inspired by M. C. Escher and Victor Vasarely

G.3 The student will solve practical problems involving complementary, supplementary, and congruent angles that include vertical angles, angles formed when parallel lines are cut by a transversal, and angles in polygons.
Geometry: Parallel Lines -- Math for Morons Like Us
Vertical Angle Theorem Proof
Linear Pair Theorem Proof
Angles and Angle Terms
Interior Angles Theorer Proof
Angles & Their Measures

Euclid's Elements, Book I, Proposition 27

G.4 The student will use the relationships between angles formed by two lines cut by a transversal to determine if two lines are parallel and verify, using algebraic and coordinate methods as well as deductive proofs.
Math Forum - Ask Dr. Math -- Geometry Proofs with Lines
Congruent Triangles
Congruent Triangles
Congruent Triangles
Congruent Triangles Part 2
Similar Triangles
Similar Triangles
Euclid's Elements, Book VI, Proposition 19

G.5 The student will

investigate and identify congruence and similarity relationships between triangles; and Math Forum - Ask Dr. Math -- Congruence and Triangles
Congruent Triangles
Inequality in a Triangle
Triangle Inequality
prove two triangles are congruent or similar given information in the form of a figure or statement, using algebraic and coordinate as well as deductive proofs.

G.6 The student, given information concerning the lengths of sides and/or measures of angles, will apply the triangle inequality properties to determine whether a triangle exists and to order sides and angles. These concepts will be considered in the context of practical situations.
Geometry : Triangle Inequality - Math for Morons Like Us

G.7 The student will solve practical problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry. Calculators will be used to solve problems and find decimal approximations for the solutions.

G.8 The student will

investigate and identify properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals;
prove these properties of quadrilaterals using algebraic and coordinate as well as deductive proofs; and
use properties of quadrilaterals to solve practical problems.

G.9 The student will use measures of interior and exterior angles of polygons to solve problems. Tessellations and tiling problems will be used to make connections to art, construction, and nature.

G.10 The student will investigate and use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles. Problems will include finding the area of a sector and applications of architecture, art, and construction.

G.11 The student will construct, using a compass and straightedge, a line segment congruent to a given line segment, the bisector of a line segment, a perpendicular to a given line from a point not on the line, a perpendicular to a given line at a point on the line, the bisector of a given angle, and an angle congruent to a given angle.
Geometric Constructions
GRACE - Graphical Ruler and Compass Editor

G.12 The student will make a model of a three-dimensional figure from a two-dimensional drawing and make a two-dimensional representation of a three-dimensional object. Models and representations will include scale drawings, perspective drawings, blueprints, or computer simulations.

G.13 The student will use formulas for surface area and volume of three-dimensional objects to solve practical problems. Calculators will be used to find decimal approximations for results.

G.14 The student, given similar geometric objects, will use proportional reasoning to solve practical problems; investigate relationships between linear, square, and cubic measures; and describe how changes in one of the measures of the object affect the others.

G.15 The student will

draw a system of vectors and find the resultant graphically, write the components of a vector as a column matrix, and find the resultant by matrix addition; and
solve practical problems using a system of vectors.