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# Investigation: 2D SHAPES

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## Nat Bannister

on 31 August 2015

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#### Transcript of Investigation: 2D SHAPES

Investigation: 2D SHAPES
CLUES:
The police have collected a list of clues about the features of the suspect. They are some of the properties of the 2D shape.

Let's investigate different types of properties:
BRAINSTORM:
Can you think of any properties of our suspects before we look at the clues?
POLICE RECORD:
Ongoing investigation:
A 2D shape robbed a bank and the police are trying to investigate which shape is to blame.
The police have found 4 possible suspects, and the only evidence collected is a few properties of the shape provided by the onlookers.
THE FOUR SUSPECTS:
Will you help the police achieve justice?
Suspect 1
Suspect 2
Suspect 3
Suspect 4
Property: opposite sides are parallel
Suspect 1
Suspect 2
Suspect 3
Suspect 4
Suspect 1
Suspect 2
Suspect 3
Suspect 4
PROPERTY: Equal angles
Suspect 1
Suspect 2
Suspect 3
Suspect 4
The sides of a shape a parallel when a side will always be an equal distance from another side; never connecting at any point
Which of our suspect shapes have parallel sides?
Think: Which 2D shapes have two sets of parallel lines?
PROPERTY: Sides are equal
Sides of a 2D shape are equal when they are the same distance in length -- let's measure!
1 pair of sides is equal
2 pairs of sides are equal
All 3 sides are equal
What's the name of a triangle with 3 equal sides?
1 pair of sides are parallel
Both pairs of sides are parallel
YOU ARE ARRESTED!
CASE SOLVED
How did its properties link to the clues?
Criminal:
THE SQUARE.
Crime:
Robbed a bank.
Evidence that it was the square:

2 pairs of parallel sides
2 pairs of opposite sides are equal
All angles are equal
All angles are right angles

Punishment:
Prison

"000" -- A NEW CLUE!
How do we link the clues to a right-angled triangle?
What are the properties of different triangles?
Information has just been received that a fifth suspect has just been found for the Case of the Bank Robbery...
Suspect 5
How many pairs of equal angles do these suspect shapes have?
Let's count...
Let's think:
BRAINSTORM:
What are some other properties of 2D shapes?
Opposite sides are parallel
Sides are equal
Pairs of angles are equal
Number of sides
Number of vertices
Types of angles in the shape [right angles, acute angles, obtuse angles]
THE EVIDENCE:

- At least 1 pair of parallel sides
- At least 1 pair of opposite angles are equal
- 2 pairs of equal sides
Who is to blame?
Trapezium (regular)
1 pair of parallel sides
1 pair of opposite sides are equal
2 pairs of opposite angles are equal
1 pair obtuse a and 1 pair of acute angles
Triangle (equilateral)
No parallel sides
All sides are equal
All angles are equal
All angles are acute
Square
2 pairs of parallel sides
2 pairs of opposite sides are equal
All angles are equal
All angles are right angles
Rhombus (regular)
2 pairs of parallel sides
2 pairs of opposite sides are equal
2 pairs of opposite angles are equal
1 pair of angles is acute; 1 pair of angles is obtuse
According to onlookers, this is the list of some of the properties of the criminal shape.
"000" NEW CLUE!
New evidence has just come in:
The suspect has
four equal angles!
Who is to blame?
Trapezium (regular)
1 pair of parallel sides
1 pair of opposite sides are equal
2 pairs of opposite angles are equal
1 pair of angles is acute; 1 pair of angles is obtuse
Triangle (equilateral)
No parallel sides
All sides are equal
All angles are equal
All angles are acute
Square
2 pairs of parallel sides
2 pairs of opposite sides are equal
All angles are equal
All angles are right angles
Rhombus
2 pairs of parallel sides
2 pairs of opposite sides are equal
2 pairs of opposite angles are equal
1 pair of angles is acute; 1 pair of angles is obtuse
What properties of the suspects clash with the evidence?
What properties of the suspects clash with the evidence?
But what is a "property" of a shape?
A property of a shape is a
common feature or characteristic
of a type of shape
Suspect 1
Suspect 2
Suspect 3
Suspect 4
Think: What types of angles are each of these pairs? Right-angled, acute or obtuse?
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