1. Transformations

2. What are transformations?
Any movement of a shape is called a transformation
There are 4 types
Reflection
Translation
Rotation
Enlargement

3. 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

4. Questions Which of the following shapes are congruent?
A and G D and I E and J C and H

5. Congruent Triangles Three sides are the same length
Two sides and one angle the same
Two angles are the same

6. Questions Yes there is one right angle and two sides the same length
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

7. Reflections
A reflected object has an image on the other side of the line of reflection
Image
Object
Line of Reflection

8. 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

9. 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)

10. 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

11. 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)

12. 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

13. 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

14. Question Enlarge triangle ABC by a scale factor of 2
Draw line from O through each of the point A, B and C
Double the distance from O to A
Plot Point A’
Repeat for B
And C
Join up these points to make the enlarged shape A’ C’ B’

15. Similar Objects
If two objects have the same shape, but are different sizes they are similar
These triangles are similar

16. Similar Triangles
Two triangles are similar if they have the same angles

17. Corresponding Angles
On these similar triangles β and Ө angles are the same

18. 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)

19. Congruent Triangles