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Transformations. What are transformations?. 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.
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What are transformations? • 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 GD and IE and JC 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 Image Object 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 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’
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)
