iShortcut Geometry Vol. 2: Triangles

kjhunjhnuwala, Dec 15, 2015

https://itunes.apple.com/us/book/ishortcut-geometry-vol.-2/id541468728?ls=1 All too often students memorize concepts without fully understanding how they work. This method of learning is often frustrating and unsatisfying. IShortcut is different. IShortcut simplifies fundamental concepts in Geometry by providing a range of interactive diagrams, illustrations, and figures. After each lesson, test your knowledge with review questions. Don’t struggle reading lengthy explanations. Learn by engaging with interactive diagrams. Each diagram gives you the ability to manipulate visuals. As you transform the visual, you can see how variables, and triangles change. After using this system, you’ll have a strong understanding of these essential concepts. This book is suitable for grades 6 and higher and is at the level of high school geometry. If a picture is worth a thousand words, then an interactive diagram is worth a thousand pictures. Don’t waste time trying to visualize the concept in your head. Simply engage with this system and master geometry.

Table of Contents

  1. Triangle Types
    1. Triangle
    2. Sum of Measures of Angles of a Triangle
    3. Exterior Angle Theorem
    4. Angle to Length Relationship of Triangle
    5. Scalene Triangle
    6. Isosceles Triangle
    7. Equilateral Triangle
    8. Acute Triangle
    9. Obtuse Triangle
    10. Right Angle Triangle
  2. Pythagorean Theorem
    1. Pythogorean Theorum
    2. Triangle Lengths Relationship
    3. 3-4-5 Triangle
    4. 90-45-45 Triangle
    5. Square Diagonal
    6. Two 30-60-90 triangles in equilateral triangle
    7. 30-60-90 Triangle
    8. Inequality Theorem - Difference
    9. Inequality Theorem - A problem
  3. Triangle Area and Perimeter
    1. Triangle Perimeter
    2. Area of Triangle
    3. Area of Equilateral Triangle
    4. Heron’s Formula
  4. Triangle Similarity
    1. Similar Triangles
    2. Similar Triangle Area
  5. Using Algebra
    1. 45-45-90 Triangle
    2. Pythagorean Theorem. 3x-4x-5x Triangle
    3. Triangle Angles Relationship
  6. Where to get book?
    1. iShortCut Geometry Vol. 2: Triangle

1.

Triangle Types

  • 1. Triangle
  • 2. Sum of Measures of Angles of a Triangle
  • 3. Exterior Angle Theorem
  • 4. Angle to Length Relationship of Triangle
  • 5. Scalene Triangle
  • 6. Isosceles Triangle
  • 7. Equilateral Triangle
  • 8. Acute Triangle
  • 9. Obtuse Triangle
  • 10. Right Angle Triangle

1.1.

Triangle

Move points A, B, and C to see what a triangle is
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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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2.

Pythagorean Theorem

  • 1. Pythogorean Theorum
  • 2. Triangle Lengths Relationship
  • 3. 3-4-5 Triangle
  • 4. 90-45-45 Triangle
  • 5. Square Diagonal
  • 6. Two 30-60-90 triangles in equilateral triangle
  • 7. 30-60-90 Triangle
  • 8. Inequality Theorem - Difference
  • 9. Inequality Theorem - A problem

2.1.

Pythogorean Theorum

Move points A and B.

Suppose a, b, c are the sides of right angle triangle ABC, then Pythagorean Theorem states that: a^2 + b^2 = c^2
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2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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3.

Triangle Area and Perimeter

  • 1. Triangle Perimeter
  • 2. Area of Triangle
  • 3. Area of Equilateral Triangle
  • 4. Heron’s Formula

3.1.

Triangle Perimeter

Move Points A, B and C

Perimeter of a triangle is the sum of lengths of all the sides. Perimeter = a + b + c.
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3.2.

–

3.3.

–

3.4.

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4.

Triangle Similarity

  • 1. Similar Triangles
  • 2. Similar Triangle Area

4.1.

Similar Triangles

Move Points A, B and C

Triangle ABC and DEF are similar because, the corresponding angles, A = D and B = E and C = F
– kjhunjhnuwala

4.2.

–

5.

Using Algebra

  • 1. 45-45-90 Triangle
  • 2. Pythagorean Theorem. 3x-4x-5x Triangle
  • 3. Triangle Angles Relationship

5.1.

45-45-90 Triangle

Move point A and C. Try to get x = 1, 2, 3, 4

When x = 2, a:b:c = 2:2:√8 because 2*1:2*1:2*√2 using 1x:1x: √2 x.
– kjhunjhnuwala

5.2.

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5.3.

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6.

Where to get book?

  • 1. iShortCut Geometry Vol. 2: Triangle

6.1.

iShortCut Geometry Vol. 2: Triangle

https://itunes.apple.com/book/ishortcut-geometry-vol.-2/id541468728?mt=11
– kjhunjhnuwala

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