Honors Geometry

Mr. DeVizia, homework hotline #7067

I. Geometric number patterns, recursive and explicit definitions

A. Triangular numbers

B. Square numbers

C. Exponential Growth

D. Logistic Growth

E. Pascal’s Triangle

F. Fibonacci Numbers

II. Probability and Statistics

A. Probability

i. Sample Space/Basic Probability

ii. Multiplication Principle

iii. Permutations and Combinations

iv. Binomial Probability

v. Probability Distributions/Frequency Distributions

B. Descriptive One-Variable Statistics

i. Mean

ii. Std. Dev.

C. Intro. to Inference; T-tests

i. Hypothesis testing

ii. Two-sample t-tests

D. Correlation/Regression

i. Linear Regression T-Test

ii. Measuring Correlation

iii. Linear Regression

E. X² Tests

i. X² Test for Goodness of Fit

ii. X² and Fitting a Binomial Probability Distribution

iii. X² Contingency Tests

III. Logic

A. Propositions and Operations

i. negation

ii. conjunction

iii. disjunction

B. Truth tables

C. Conditional statements

D. Converse, inverse, and contrapositive

E. Quantifiers

F. Algebraic properties

i. properties of equivalence relations

ii. properties of equality

G. Direct proof

H. Deductive systems

IV. Introduction to Euclidean Geometry and terminology

A. Points, lines, planes, and segments

B. Rays, angles and angle pairs

C. Parallel and perpendicular lines

V. Triangles and congruence

A. Correspondence and congruence

B. Proving triangles congruent

C. Using congruent triangles

D. Combined congruence proofs

E. Medians, altitudes, and bisectors

F. Auxiliary lines in proofs

G. Proving right triangles congruent

VI. Parallelism and angle measures

A. Lines, planes, and transversals

B. Parallel lines and angles

C. Indirect Reasoning

D. Proving lines parallel

E. Parallel lines and angles in a triangle

F. Polygons and angle measures

VII. Quadrilaterals

A. Definitions and relationships

B. Trapezoids and their properties

C. Parallelograms and their properties

D. Special parallelograms and their properties

VIII. Similarity

A. Ratio and proportion

B. Similar polygons

C. Similar triangles and proof

D. Proportional segments

IX. Right triangles

A. The “altitude-to-hypotenuse” lemmas

B. The Pythagorean Theorem

C. Converse and corollaries of the Pythagorean Theorem

D. Pythagorean triples

E. Special right triangles

F. Trigonometric solution of right triangles and applications

X. Circles

A. Circles and segments

B. Tangents

C. Arcs, chords, and central angles

D. Inscribed angles

E. Tangents, secants, and angles

XI. Area

A. Area concepts and formulas

1. Squares and rectangles

2. Parallelograms and triangles

3. Kites

4. Trapezoids

5. Regular polygons

6. Circles, sectors; circumference and arc length

B. Problem solving in compound figures

C. Area and similarity

D. Geometric probability

XII. Solids; area and volume

A. The Platonic Solids

B. Surface area and volume

1. Prisms and cylinders

2. Pyramids and cones

3. Spheres

C. Volume and similarity

XIII. Fractal Geometry*

A. Geometric iteration

i. the Koch Snowflake, Peano Curve, et. al.

ii. the Sierpinski Triangle and the Cantor Set

B. Fractal dimension

C. Numerical iteration

D. Iterated Function Systems (the Chaos Game)

E. Pascal’s Triangle and the Sierpinski Triangle

IV. Graph Theory*

A. Graphs and modeling

B. Eulerian graph theory

C. Hamiltonian graph theory

i. MST, Kruskal and Prim algorithms

ii. TSP, "brute force" vs. Nearest-Neighbor algorithm

*Topic to be included if time allows