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Transformations
What are transformations?
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•
1.
2.
3.
4.
Any movement of a shape is called a
transformation
There are 4 types
Reflection
Translation
Rotation
Enlargement
Congruent Shapes
• A congruent shape is the same shape
and size to another shape
•These are congruent shapes because they are the
same shape and size
•These are similar shapes because they are the
same shape, but have different sizes
Questions
• Which of the following shapes are
congruent?
A and G
D and I
E and J
C and H
Congruent Triangles
• Three sides are the same length
•
Two sides and one angle the same
•
Two angles are the same
Questions
• Are these triangles congruent?
• Yes there is one right angle and two sides the same
length
•Are these triangles congruent?
•No, the 7cm is in different positions in both triangles, we
only know that 2 angles are the same
Reflections
• A reflected object has an image on the
other side of the line of reflection
Object
Image
Line of Reflection
Finding the Line Of Reflection
• The line of reflection if halfway between
the object and the image
Draw a line between A and A’
Find the bisector of this line
This is the Line of Reflection
Translations
• A translation is a movement in a straight line
• Describe this translation
The original triangle is ABC
It move to A’B’C’
Look at A
How far across X has it
moved?
X= -5
How far has it moved up the y
axis?
Y= 3
So the translation is (-5,3)
Rotations
• A rotation turns a shape through an angle
about a fixed point
• The fixed point is called the centre of rotation
The original shape is ABC
It has been rotated 90°
about the origin
The origin is X=0, y=0
Finding the Centre of Rotation
• Find two matching point on
your shapes
• E.g. A and A’
• Draw a line between the
two
• Bisect this line
• Do the same for another pair
of points
• B and B’
• Repeat what you did with the
A points
• Where the two bisectors
cross is the centre of origin
• (0,-1)
Enlargements
• An enlargement changes the size of the object
• The scale factor tells you how much bigger or smaller
the object becomes
• Enlargements can be done about a centre
The scale factor is ½
A to C = 2
But A’ to C’ = 1
Centre
Question
• Where is the centre and what is the scale
factor for this enlargement?
The origin is
where the
black dot is
The scale
factor is 3
3
9
Question
• Enlarge triangle ABC by a scale factor of 2
Draw line from O
through each of the point
A, B and C
A’
C’
Double the distance from
O to A
Plot Point A’
Repeat for B
And C
B’
Join up these points to
make the enlarged
shape
Similar Objects
• If two objects have the same shape, but
are different sizes they are similar
These triangles are similar
Similar Triangles
• Two triangles are similar if they have the
same angles
Corresponding Angles
• On these similar triangles β and Ө angles
are the same
Congruent Triangles
•
For two triangles to be congruent they must have matching
angles and sides
•
There are four rules;
1. All three pairs of sides are the same
•
(SSS)
2. The right angle, hypotenuse and one other side are equal
•
(RHS)
3. Two pairs of corresponding sides are equal and the angle
between them is the same
•
(SAS)
4. Two pairs of angles are equal and a pair of corresponding sides
are equal
•
(AAS)
Congruent Triangles