Mathematical Investigation

1
Mathematical Investigation
CORNERS

• Prepared by Jasmine Mel

2
Types of Corners

• Reflex corners that are gt 180o but lt 360o
• Acute corners that are lt 90o
• Obtuse corners that are gt 90o but lt 180o
• Right angled equal to 90o

3
This is an irregular octagon. It has two types of
corners. They are Reflex and Right angled
270 degrees
90 degrees
4
Regular Octagon

• Has all sides equal
• All outside corners are reflex corners
• Angles on the outside are equal to 225o
• Angles on the inside are equal to 135o

5
Irregular Octagons Same Sides
All these shapes have 6 reflex and 2 right angled
corners on the outside and 6 right angled and 2
reflex corners on the inside
6
Irregular Octagons Different Corners
Irregular octagons can have all the different
types of corners. This just depends on how you
manipulate the sides
7

• Irregular octagons with the same corners
• Always have six reflex angles and two right
  angles on the outside
• And
• Always have six right angles and two reflex
  angles on the inside
• Irregular octagons with different corners
• Can have all the different types of corners

8
What If the Shape Is Made 3D?

• Octagonal prism
• Decahedron
• All the corners are the same as the 2D shape
• Angles remain the same as 2D shape

9
What If Original Shape Is 3D?

• The corners and angles are still the same as the
  2D shape
• The shape is now a decahedron and a octagonal
  prism

10
Shape Made With Scaled Sides
6cm 3cm

• 7 out of 8 sides are used to make this square
• The side left over is the 4cm side
• A square has 4 lines of symmetry
• A square has 4 identical reflex corners on the
  outside and 4 right angled corners on the inside

9cm
6cm 2cm 1cm
9cm
11
Irregular Shape Using Scaled Sides

• This is a polygon
• This shape has 2 obtuse corners and 6 reflex
  corners

12
What If Shape Is Dissected?

• Many different shapes can be made
• One example is that the shape can make 3
  trapeziums

13
Conclusion

• In the shape, it was investigated that the two
  types of corners are reflex and right angled
• Through mathematical investigation using drape,
  protractors, rulers, technology, and other
  methods it was discovered that 4 types of corners
  exist (reflex, acute, right angled and obtuse)