Maths · OCR Paper 2
Transformations and Similarity
The transformation skills tested on OCR Paper 2: reflections, translations, rotations and enlargements on a grid, combined transformations, and congruent and similar shapes, all done without a calculator.
Lessons
Ticks are remembered on this device only.
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1
Reflections and Translations
Reflecting shapes in mirror lines, translating them with column vectors, and describing each transformation fully.
9 terms -
2
Rotations
Rotating shapes about a centre, describing a rotation fully, and finding the centre of a rotation.
9 terms -
3
Enlargements
Enlarging shapes by whole-number, fractional and negative scale factors, and describing an enlargement fully.
9 terms -
4
Combined Transformations
Carrying out one transformation after another, finding the single equivalent transformation, and spotting invariant points.
9 terms -
5
Congruence and Similarity
Proving triangles congruent, finding missing lengths in similar shapes, and using scale factors for length, area and volume.
9 terms
Key terms in this chapter
All 45, gathered from every lesson.
- Transformation
- A change in the position or size of a shape.
- Object
- The original shape before a transformation.
- Image
- The shape after a transformation.
- Reflection
- A transformation that flips a shape over a mirror line.
- Mirror line
- The line over which a shape is reflected.
- Translation
- A transformation that slides a shape without turning or flipping it.
- Column vector
- A pair of numbers, one above the other, that gives a move right or left and up or down.
- Congruent
- Having exactly the same size and shape.
- Orientation
- The way round a shape faces.
- Rotation
- A transformation that turns a shape about a fixed point.
- Centre of rotation
- The fixed point about which a shape is turned.
- Clockwise
- The direction of the hands of a clock.
- Anticlockwise
- The direction opposite to the hands of a clock.
- Quarter turn
- A rotation of \(90^\circ\).
- Half turn
- A rotation of \(180^\circ\).
- Angle of rotation
- The size of the turn, in degrees.
- Perpendicular bisector
- A line that cuts another line in half at right angles.
- Image
- The shape after a transformation.
- Enlargement
- A transformation that changes the size of a shape by a scale factor.
- Scale factor
- The number by which every length of a shape is multiplied.
- Centre of enlargement
- The fixed point from which an enlargement is measured.
- Similar
- The same shape but not necessarily the same size.
- Congruent
- Having exactly the same size and shape.
- Corresponding sides
- Sides in the same position on two similar shapes.
- Image
- The shape after a transformation.
- Ray
- A straight line drawn from the centre through a point and its image.
- Negative scale factor
- A scale factor that puts the image on the opposite side of the centre.
- Combined transformation
- One transformation followed by another.
- Invariant
- Not changed by a transformation.
- Invariant point
- A point that stays in the same place under a transformation.
- Single transformation
- One transformation that has the same effect as a combination.
- Reflection
- A transformation that flips a shape over a mirror line.
- Rotation
- A transformation that turns a shape about a centre.
- Translation
- A transformation that slides a shape.
- Parallel lines
- Lines that stay the same distance apart and never meet.
- Congruent
- Having exactly the same size and shape.
- Congruent
- Exactly the same size and shape.
- Similar
- The same shape, with corresponding sides in the same ratio.
- Scale factor
- The ratio of corresponding lengths in similar shapes.
- Corresponding sides
- Sides in the same position on two similar shapes.
- SSS
- A condition for congruence: three pairs of equal sides.
- SAS
- A condition for congruence: two sides and the angle between them equal.
- ASA
- A condition for congruence: two angles and a side equal.
- RHS
- A condition for congruence of right-angled triangles: hypotenuse and one other side equal.
- Proof
- A logical argument that shows a statement is true, with a reason for each step.