Algebra 1 with Geometry

Andre Mathurin, Oct 16, 2016

Table of Contents

  1. Number Patterns
  2. Figurative Numbers
    1. Polygonal numbers
    2. square numbers
    3. triangular numbers
  3. Exploring Circles with Right Triangles
    1. Pythagorean and similar triangles.
    2. Pythagorean Theorem and Circles
    3. Circle Terminology
    4. Right Triangle Trigonometry Ratios

1.

Number Patterns


    This chapter does not contain any resources yet.

2.

Figurative Numbers

  • 1. Polygonal numbers
  • 2. square numbers
  • 3. triangular numbers

2.1.

Polygonal numbers

Use the yellow slider to explore a sequence of triangular numbers T(n) and square numbers S(n). How does T(n) depends on T(n-1) and n? What is the value of T(100)? How does S(n) depends on S(n-1) and n? What is the value of S(100)? The applet will show you the first three hexagonal numbers H(1), H(2) and H(3). Can you write an expression for H(n)? Why do all polygonal numbers seem to increase quadratically?
– Judah L Schwartz

2.2.

–

2.3.

–

3.

Exploring Circles with Right Triangles

  • 1. Pythagorean and similar triangles.
  • 2. Pythagorean Theorem and Circles
  • 3. Circle Terminology
  • 4. Right Triangle Trigonometry Ratios

3.1.

Pythagorean and similar triangles.

A tool to visualize a proof of the Pythagorean Theorem using similar triangles.
– Ted Coe

3.2.

–

3.3.

–

3.4.

–

Information