GCSE Higher Ch5 Angles & Trigonometry

Nicola Trubridge, May 2, 2018

Table of Contents

  1. Angle properties triangles
    1. Angles in a triangle add up to 180°
    2. Angles around lines
  2. Angle properties quadrilaterals
  3. Interior and exterior angles
    1. Interior and Exterior Angles in Regular Polygons
    2. Sum of the Interior Angles of a Polygon
    3. Exterior Angles of Polygons
    4. Sum of exterior angles of a polygon
    5. Investigate the sum of interior angles in polygons
    6. Sum of interior angles of polygons
    7. Polygon Sum of Interior Angles
    8. Sum of Interior Angles of Polygons
    9. Interior and exterior angles in regular polygons
    10. Exterior Angles of Polygons (Hexagon)
    11. Inscribed Regular Polygons in a Circle
  4. Pythagoras
    1. Pythagorean Fractal Tree
    2. Proof of Pythagoras' theorem (Henry Perigal)
    3. Perigal's Dissection
    4. Pythagoras Theorem
    5. Pythagorean Theorem Proof #6
    6. Garfield proof of Pythagoras
    7. Puzzle proof of the Pythagorean Theorem
  5. Right angled trigonometry
    1. Right Triangle Trigonometry: Intro
    2. Trig ratios
    3. Right angle triangle ratios
    4. Basic Trig Question Generator (Lengths)
    5. Right Triangle Trig: Solving for Sides (2)
    6. Identifying Sides of Right Triangles

1.

Angle properties triangles

  • 1. Angles in a triangle add up to 180°
  • 2. Angles around lines

1.1.

Angles in a triangle add up to 180°

Drag the points to see how the angles change.

Angles in a triangle add up to 180°
– John Tranter

1.2.

–

2.

Angle properties quadrilaterals


    This chapter does not contain any resources yet.

3.

Interior and exterior angles

  • 1. Interior and Exterior Angles in Regular Polygons
  • 2. Sum of the Interior Angles of a Polygon
  • 3. Exterior Angles of Polygons
  • 4. Sum of exterior angles of a polygon
  • 5. Investigate the sum of interior angles in polygons
  • 6. Sum of interior angles of polygons
  • 7. Polygon Sum of Interior Angles
  • 8. Sum of Interior Angles of Polygons
  • 9. Interior and exterior angles in regular polygons
  • 10. Exterior Angles of Polygons (Hexagon)
  • 11. Inscribed Regular Polygons in a Circle

3.1.

Interior and Exterior Angles in Regular Polygons

Interior and Exterior Angles in Regular Polygons

Label all the angles that you can [color=#0a971e]Adapted by N.Trubridge[/color]
– Jonathan Robinson, Nicola Trubridge

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

3.10.

–

3.11.

–

4.

Pythagoras

  • 1. Pythagorean Fractal Tree
  • 2. Proof of Pythagoras' theorem (Henry Perigal)
  • 3. Perigal's Dissection
  • 4. Pythagoras Theorem
  • 5. Pythagorean Theorem Proof #6
  • 6. Garfield proof of Pythagoras
  • 7. Puzzle proof of the Pythagorean Theorem

4.1.

Pythagorean Fractal Tree

– Nicola Trubridge, xristos pazol

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

5.

Right angled trigonometry

  • 1. Right Triangle Trigonometry: Intro
  • 2. Trig ratios
  • 3. Right angle triangle ratios
  • 4. Basic Trig Question Generator (Lengths)
  • 5. Right Triangle Trig: Solving for Sides (2)
  • 6. Identifying Sides of Right Triangles

5.1.

Right Triangle Trigonometry: Intro

[color=#980000][b]Key Question: [/b][/color] [br][br][color=#000000]Hopefully, you noticed that when you keep the blue angle fixed and move only the white vertices, the value of each ratio never changes (even though the side lengths do)! [/color][color=#ff00ff][i]Why does this occur? [/i] Explain! [/color]
– Nicola Trubridge, Tim Brzezinski

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

Information