Quadrilateral Tessellations with M.C. Escher
The artist M C Escher
created these
tessellations
All quadrilaterals tessellate
Is this sometimes, always
or never true?
How can you check?
You have:
Square dotty paper
Scissors
Glue
Which quadrilaterals tessellate?
Choose a quadrilateral to try. Draw 4
congruent
shapes and see if they tessellate.
•
Square
•
Rectangle
•
Parallelogram
•
Rhombus
•
Trapezium
•
Kite
•
‘Irregular’ quadrilateral
https://www.geogebra.org/m/BpZa7hy8
a
b
c
d
To show that
quadrilaterals
always tessellate,
we can use letters
to represent the
angles.
Write a maths
sentence using the
letters in the
diagram.
a
b
c
d
Imagine tracing the
quadrilateral and
rotating it to make
the other tiles.
What would the
missing letters be?
?
?
?
a
b
c
d
What do angles
around a point add
up to?
b
c
d
a
b
c
d
We know that
a
+
b
+
c
+
d
= 360°
Which means that
quadrilaterals will
always tessellate.
b
c
d
a
b
c
d
Write an explanation
of why quadrilaterals
tessellate in your
books.
Use the tessellations
of your tiles.
b
c
d
Dive into the world of quadrilateral tessellations with the captivating art of M.C. Escher. Discover which quadrilaterals tessellate and why they always do so. Use visual aids and geometric concepts to engage in hands-on exploration. Unveil the beauty of tessellation patterns and angles through interactive activities.
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Presentation Transcript
The artist M C Escher created these tessellations
All quadrilaterals tessellate Is this sometimes, always or never true?
How can you check? You have: Square dotty paper Scissors Glue
Which quadrilaterals tessellate? Choose a quadrilateral to try. Draw 4 congruent shapes and see if they tessellate. Square Rectangle Parallelogram Rhombus Trapezium Kite Irregular quadrilateral
https://www.geogebra.org/m/BpZa7hy8 https://www.geogebra.org/m/BpZa7hy8
To show that quadrilaterals always tessellate, we can use letters to represent the angles. b a c Write a maths sentence using the letters in the diagram. d
Imagine tracing the quadrilateral and rotating it to make the other tiles. ? ? b a What would the missing letters be? ? c d
What do angles around a point add up to? b c b a d c d
We know that a + b + c + d = 360 b Which means that quadrilaterals will always tessellate. c b a d c d
Write an explanation of why quadrilaterals tessellate in your books. b c b a d Use the tessellations of your tiles. c d
