[PDF] Angle, symmetry and transformation

Angle, symmetry and transformation

Alternate angles Where two straight lines are cut by a third line (called the transversal), as in the diagram, the angles a and b (also c and d) are alternate If the two straight lines are parallel, then the alternate angles are equal in size Angle An angle measures the amount of ‘turning’ between two

STRAND F: GEOMETRY Angles and Symmetry

Find the sizes of angles a and b in the diagram below Solution First consider the quadrilateral All the angles of this shape must add up to 360°, so 60 120 80 360 oo o o+++=a 260 360 oo+=a a = 360 260− oo = 100 o Then consider the straight line formed by the angles a and b These two angles must add up to 180 o so, ab+=180 o but a =100o

UNIT 31 Angles and Symmetry CSEC Revision Test

Angles marked p and q are equal (a) What geometrical name is given to this type of equal angles? (b) Write down the size of angle r (c) (i) Write down the size of angle x (ii) What geometrical name is given to the pair of angles x and q? (4 marks) UNIT 31 Angles and Symmetry CSEC Revision Test 45˚ 20˚ 70˚ x y p x r q 80˚ Diagram not

Two-Dimensional Shapes, Angles, Symmetry

Two-Dimension Shapes, Angles, and Symmetry Grade: 4 Mathematical goals This lesson is intended to help you assess how well students are able to: Identify and sort quadrilaterals based on their properties and attributes Identify and classify angles and identify the angles in two-dimensional figures

7 Symmetry and Group Theory - University of Pennsylvania

An equilateral triangle can be rotated by 120 , 240 , or 360 angles without really changing it If you were to close your eyes, and a friend rotated the triangle by one of those angles, then after opening your eyes you would not notice that anything had changed In contrast, if that friend rotated the triangle

ANGLES ET SYMETRIE

Deux angles sont complémentaires lorsque la somme de leurs mesures est égale à 90° Deux angles sont supplémentaires lorsque la somme de leurs mesures est égale à 180° 3) Angles alternes-internes, angles correspondants Deux droites coupées par une sécante forment avec cette sécante deux paires d’angles alternes-internes et

Terms Illustrations Acute angle An angle greater than 0° and

Two angles which add together to 90° Each is the ‘complement’ of the other Coordinate system A system which uses one or more numbers, or coordinates, to determine the position of a point in space e g (4,8) on a grid with a horizontal and vertical axis The y axis is vertical and the x axis is horizontal Corresponding angles

Transformer une figure par symétrie, translation ou rotation

2 L homothétie conserve les angles, PAUL est un rectangle, donc MIRO est un rectangle 3 MIRO est l image de PAUL par une homothétie de rapport 3 , donc : PMIRO = 3 × P PAUL = 3 × 24 = 72 cm Le périmètre de MIRO est égal à 72 cm 4 AireMIRO = 3 2 × Aire PAUL = 9 × 32 = 288 cm 2 L aire de MIRO est égale à 288 cm 2

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Angle, symmetry and transformation

1 | Numeracy and mathematics glossary

Term Definition Illustrations

Acute angle An angle greater than 0° and less than 90°. Alternate angles Where two straight lines are cut by a third line (called the transversal), as in the diagram, the angles a and b (also c and d) are alternate. If the two straight lines are parallel, then the alternate angles are equal in size. Angle straight lines that meet at a vertex (point). Angles can be classified by their size e.g. obtuse, acute, reflex, right angle etc. They are usually measured in degrees (°) using a protractor.

Angle, symmetry and transformation

2 | Numeracy and mathematics glossary

Axis A fixed, reference line from which locations, distances or angles are taken. Usually grids have an x axis and y axis. Bearings A bearing is used to represent the direction of one point relative to another point. It is the number of degrees in the angle measured in a clockwise direction from the north line. In this example, the bearing of A from B is 205°. Bearings are commonly used in navigation.

Compass

(in directions) An instrument containing a magnetised pointer which shows the direction of magnetic north and bearings from it. Used to help with finding location and directions.

Angle, symmetry and transformation

3 | Numeracy and mathematics glossary

Compass points Used to help with finding location and directions. Common points include North, East, South, West, (N, E, S, W), North East (NE), South East (SE), South West (SW) and

North West (NW) as well as

NNE (north-north-east)

ENE (east-north-east)

ESE (east-south-east)

SSE (south-south-east)

SSW (south-south-west)

WSW (west-south-west)

WNW (west-north-west)

NNW (north-north-west)

Complementary

angles Two angles which add together to 90°. Each is the

Angle, symmetry and transformation

4 | Numeracy and mathematics glossary

Coordinate system A system which usually uses numbers as coordinates to determine the position of a point in space e.g. (4,8) on a grid with horizontal (x) and vertical (y) axes.

Corresponding

angles Where two straight lines are cut by a third line (called the transversal), as in the diagram, the angles a and b (also c and d), for example, are corresponding. If the two straight lines are parallel, then the corresponding angles are equal in size.

Angle, symmetry and transformation

5 | Numeracy and mathematics glossary

Cosine function in

trigonometry ș஺ௗ௝௔௖௘௡௧ Degrees The most common unit of measurement for angles. One full turn is equal to 360 degrees, written as 360o

Directional

language The use of a variety of words to help with directions such as left, right, up, down, forwards, backwards, sideways, across, close, far, along, to, from, over, under, near, through, towards, away from, underneath, quarter turn, half turn, three quarter turn, whole turn, journey, route, clockwise, anti-clockwise, North, East, South, West, horizontal, vertical , diagonal. Exterior angle In a polygon, exterior angles are formed outside the shape between one side and the adjacent side. The angle that has to be turned at the vertex if you are travelling around a shape.

Angle, symmetry and transformation

6 | Numeracy and mathematics glossary

Half turn Rotation through 180o

180o
Hypotenuse The longest side of a right-angled triangle.

It is the side opposite the right angle.

Interior angle At a vertex of a shape, the angles that lie within it. Obtuse angle An angle greater than 90° but less than 180°.

Angle, symmetry and transformation

7 | Numeracy and mathematics glossary

Opposite angles Angles formed where two lines intersect.

Also known as vertically opposite angles.

Order (in

symmetry) The number of times a shape can be rotated and fit exactly on top of its original position within a complete turn. Parallel lines Lines are parallel if they are always the same distance apart (called "equidistant" and travel in the same direction. They will never meet.

Angle, symmetry and transformation

8 | Numeracy and mathematics glossary

Perpendicular

lines Lines that are at right angles (90°) to each other.

Positional

language The use of a variety of words to help with describe position such as over, under, above, below, top, bottom, side on, inside, outside, in front of, behind, front, back, before, after, beside, next to, in the middle of, opposite, apart, between. Protractor An instrument for measuring or drawing angles, usually in the form of a semi-circle marked with degrees along the curved edge.

Angle, symmetry and transformation

9 | Numeracy and mathematics glossary

Theorem

In a right angled triangle, the square of the long side (hypotenuse) is equal to the sum of the squares of the other two sides.

It is stated in this formula:

a2 + b2 = c2

Greek philosopher and mathematician.

Quadrant Any of the 4 areas made when we divide up a graph by an x and y axis.

Angle, symmetry and transformation

10 | Numeracy and mathematics glossary

Quarter Turn A rotation through 90 o.

Ratio The relative sizes of two or more values.

In the context of shape, a ratio can be used to describe the link between actual lengths and those on a scale model or diagram.

Reflective

Symmetry or Line

Symmetry

equal. Symmetry goes beyond simple shapes to explore real images and other forms of symmetry.

Right angle An angle of 90o.

Angle, symmetry and transformation

11 | Numeracy and mathematics glossary

Rotational

Symmetry

A shape has rotational symmetry when it fits into its own outline after a rotation. How many times this happens in a full rotation is called the order of rotational symmetry. Scale The ratio of the length in a drawing (or model) to the length of the real thing. Ratios are used to enlarge or reduce an image, drawing or model. This model car is built in the ratio 1:43 meaning the real car is

43 times bigger.

Angle, symmetry and transformation

12 | Numeracy and mathematics glossary

Scale drawings A drawing that shows a real object with accurate sizes reduced or enlarged in a certain ratio. This floorplan for a house indicates the actual measurements as well as the correct proportions for the house. Similarity Similar shapes and figures are those whose dimensions are linked using a scale factor. Sine function șை௣௣௢௦௜௧௘

Angle, symmetry and transformation

13 | Numeracy and mathematics glossary

Straight angle An angle of 180 degrees.

A straight angle lies on a straight line.

Supplementary

angles

Angles which add up to 180°.

Tangent line A tangent is a straight line that touches a circle at one point only.

Angle, symmetry and transformation

14 | Numeracy and mathematics glossary

Tangent function șை௣௣௢௦௜௧௘

Tessellation or

tiling A pattern made of identical shapes where the shapes fit together without any gaps and the shapes do not overlap.

Three quarter turn A rotation through 270 o

This is the same as three right angles (3 x 90 o). Transformation Changing a shape using rotation (turns), reflection (flips), translation (slides) or resizing it.

Angle, symmetry and transformation

15 | Numeracy and mathematics glossary

Translation

shape still looks exactly the same, just in a different place. Trigonometry Trigonometry is the study of the relationships between the sides and angles in triangles. The common functions of angles in trigonometry are sine, cosine, and tangent.

Vertex (singular) or

vertices (plural)

A point(s) where two or more straight lines meet.

Whole turn A rotation through 360 degrees. Also known as a full turn.quotesdbs_dbs8.pdfusesText_14