# Tau Geometry ...

The main focus for Tau is Geometry. We will study properties of equilateral triangles, right triangles, similar triangles, rhombus, circles, trapezoids, and regular polygons. We will learn many geometry theorems, and will work on all kinds of proofs. We will study volume, surface area, and area of complex figures. Most importantly, in this class, we don’t stay at the proof level, we solve intricate geometry problems applying the theorems learned. The SATs, and math competitions, do not have proofs, they have problems!

During the Lab hour we will do many drawing exercises using squares and compass to help students really understand the various theorems we learn, and also make them prove these theorems in paper by drawing and measuring.

**Students in this level will excel in their high school honors Geometry class.**

We will continue to work on problem solving techniques, work rate problems,compound rule of three, venn diagrams, average speed problems, number theory problems, complex algebra problems, and many other kinds of problems.

The students will review and work on more complex operations with polynomials, factoring, and will learn to find solutions of radical equations. They will work comfortably with rational expressions/equations.

Students will be solving the most difficult geometry problems from AMC10, MATHCOUNTS and select AIME problems.

We will be solving over 500+ word problems in the school year that include some of the most difficult problems from MATHCOUNTS, AMC, AIME and many problems have been taken from college level text books. We also expose take problems from high school math competitions.

### Geometry

Pythagoras theorem.

Area/perimeter of a circle.

Complementary/supplementary angles.

Angles/diagonals of a regular polygon.

Properties of similar triangles.

Properties of right triangles (90-30-60) (90-45-45).

Properties of trapezoids, rhombus, and regular polygons.

Volume/Surface Area.

### Polynomials

Factor a quadratic equation using the various methods.

Find the solutions to a quadratic equation.

Add/subtract, multiply/divide polynomials.

Use the Pascal triangle to determine the coefficients when expanding a binomial.

Solve equations involving radicals.

### Probabilities

Combinations and permutations.

Probabilities problems.

### Sequences

Complex problems involving arithmetic sequences.

Geometric sequences.

### 500+ Word Problems

Problems involving fractions/decimals/percentages.

Venn diagram problems.

Coumpound rule of three problems.

Average speed problems.

A wide range of geometry problems.

Probability problems.