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Transcript
Identify 5 right angles in the classroom? Door corner, book corners, desk corner…… 4 How many right angles are there around a point? 90 How many degrees are in a right angle? 360 How many degrees are there around a point? How many right angles are 16 there on this flag? Show respect to all other people and property Be on time to class Bring all necessary equipment to class Enter the room sensibly Listen in silence when the teacher or another student is talking Raise your hand when you want to ask or answer a question Work without disturbing others Complete all homework Vocabulary Vertex Arm C We name this angle CÂT A T Ex 25.02 Question 2,3 An angle measures the amount a line has to turn to fit onto another line We measure angles in degrees. Vocabulary to do with Angle Sizes An acute angle is between 0 and 90 degrees A right angle is 90 degrees An obtuse angle is between 90 and 180 degrees A straight angle is 180 degrees A reflex angle is between 180 and 360 degrees Do Exercise 25.05 go onto 25.06 if finished 150° Obtuse Acute Reflex Right Angle Straight 248° 105° 78° 90° 24° 348° 180° Obtuse 150° 105° Acute 78° 24° Reflex 248° 348° Right Angle90° Straight 180° We generally measure angle in degrees with a protractor 110 degrees Exercise 25.04 do any 5 Angle Jade Estimation Kate Estimation Exact size Winner Example(1 ) 45 50 42 Amy 1 2 3 4 5 6 7 8 Complementary Angles are angles that add to 90°. 55° x=? X=35° Adjacent angles on a straight line sum 1800 1200 600 Supplementary angles Activity Draw a straight line on your paper. Name each angle of your triangle. One A,B and C Tear, (or cut) the angles (corners) away from your paper and lay them out alone the line. C A B Angles in a Triangle Angles in a triangle sum 1800 1.Two different objects with acute angles 2.Four different objects with right angles 3.Two different objects with obtuse angles 4.One straight angle 5.Two different reflex angles around the room Bonus Question Can you find any angles that are complementary or supplementary? Angles around a point sum 3600 1200 a a = 80 degrees 1600 Vertically opposite angles Are opposite each other at a vertex They are equal Vertex Page 378 and 380 Exercise 25.09 and 25.10 Angles on parallel lines Transversal Corresponding angles are congruent 1000 a a = 100 degrees Co-interior angles sum 1800 g 720 g = 108 degrees k 700 Alternate angles are congruent K = 70 degrees Starter!!! 50º You can choose to do the left hand side or the right hand side. 70º B= C= C= 60º A=____ 50º B=____ C=____ 70º 30º D=____ E=____ 90º 120º A= E= A= B= 85º E= 60º D= D= 70º A=____ 110º B=____ 70º C=____ 95º D=____ 95º E=____ Page 246 Ex. 18.07 Have a counter on each of the spots. The first player can remove 1 or 2 counters off the board (if they take two they must be connecting dots.) The winner is the player who picks up the last counter!!! Play a few games and try to work out a winning strategy Name the following shapes and give examples of them from your life. Page 457 Exercise 29.01 Questions 4, 6, 9,14 and 15 4- a) 4 b) 6 c) 4 6- Draw on the board 9- Next Page 14- Tetrahedron 15- a) Trapeziums b) 12 c) Pyramid Barton, D., Alpha Mathematics Second Edition Shape No. Faces No. Edges No. Vertices a Cube 6 12 8 b Triangular Prism 5 9 6 C Hexagonal Prism 8 18 12 d Pyramid 5 8 5 e Cube where a triangular slice has been cut off. 7 15 10 •Barton, D., Alpha Mathematics Second Edition A solid made up of four identical cubes joined face to face There are eight different tetracubes Make each tetracube then draw it in your isometric paper Make sure you don’t just draw the same tetracube from a different angle Top Right Left Left Front Right 1 1 1 1 Plain View Front Right Front Left Draw your own copy of this block formation on your isometric paper Draw the front, left, right and top views Draw the plan view of the shape. Front Right Try and make this shape!!! (Then draw it) Left Top Front Right Right Left Front Left Plain View 2 2 3 1 2 Top Plain View- shows the height of different parts of the solid when viewed from above. There are also profile views which show the shape from one side only. Plain View 2 2 Left Front 3 2 1 Top Right A plan that shows all the faces of a solid. It shows how all the faces could be folded and joined to make the shape. Dashed lines show where to fold. Often tabs are included for ease of constructing the shape from the net. Make a net for a closed cube. How many faces does a closed cube have? What is the smallest number of tabs that you could use so that every joint is secure? What coloured square will be on the opposite side of the cube from the green one? Closed figures made up of straight sides. Triangle Quadrilateral Pentagon Hexagon Octagon Decagon Interior angles- are angles between the sides of the polygon on the inside. • Exterior angles- are angles found by extending the sides of the polygon. • • • Measure the exterior angles of your polygons. Add the exterior angles of each shape together. What do they add to?d Shape Total Degrees of Exterior Angles Triangle 360 Quadrilateral 360 Pentagon 360 Hexagon 360 The sum of the exterior angles of a polygon is 360°. Alternate angles When two parallel lines are cut by a third line, then angles in alternate positions equal in size. Co-interior angles When two parallel lines are cut by a third line, co-interior angles are supplementary. Angles at a point. The sum of the sizes of the angles at a point is 360 Adjacent angles on a straight line The sum of the sizes of the angles on a line is 180 degrease Adjacent angles in a right angle The sum of the size's of the angles in around different points but the same angle Vertically opposite angles Vertically opposite angles are equal in size. Corresponding angles When two parallel lines are cut by a third line, then angles in corresponding positions are equal in size. No. of sides of polygon 3 4 5 You do 6, 8, 10 Drawing ttrsgf Number of 1 2 3 triangles Degrees in a triangle sum to 180° If there are 180 degrees in a triangle how many degrees must there Be in a quadrilateral which is split into 2 triangles. The rule (n2) × 180° n is the number of sides of the polygon A polygon is called regular if all its sides are the same length and all its angles are the same size. e.g. equilateral triangle, a square or a regular pentagon. Exterior Angles Number of sides 3 4 5 6 8 Equilateral triangle Square Pentagon Hexagon Octagon Decagon Interior Angles Equilateral triangle Square Pentagon Hexagon Octagon Decagon 10 Number of sides 3 4 5 6 8 10 Sum of exterior Each exterior angles angle 36 120 0 90 36 72 0 60 36 45 0 36 36 0 36 Sum0of exterior Each exterior angles 36 180 0 360 540 720 108 0 144 0 angle 60 90 108 120 135 144 Bearings are angles which are measured clockwise from north. They are always written using 3 digits. The bearings start at 000 facing north and finish at 360 facing north. Bearings 045 120 180 270 A translation is a movement in which each point moves in the same direction by the same distance. To translate an object all you need to know is the image of one point. Every other point moves in the same distance in the same direction. A B G A' B’ G’ F F’ E E’ D C D’ C’ In a reflection, and object and its image are on opposite sides of a line of symmetry. This line is often called a mirror line. m m m If a point is already on the mirror line, it stays where it is when reflected. These points are called invariant points. m m Ex 26.03 2 of 1a, b, c or d. Page397 26.04 Question 2, 7 and 8. Page 401 & 402 Any three questions from 26.05. Page 404 Rotation is a transformation where an object is turned around a point to give its image. Each part of the object is turned through the same angle. To rotate an object you need to know where the center of rotation is and the angle of rotation. This can be given in degrees or as a fraction such as a quarter turn. The direction the object is turned can be either clockwise or anti-clockwise. A B C D C’ D’ A’ B’ Rotations are always specified in the anti clockwise direction 270º Anti clockwise is _______ clockwise 180º Anti clockwise is ______ clockwise 340º Anti clockwise is _______ clockwise In rotation every point rotates through a certain angle about a fixed point called the centre of rotation. Rotation is always done in an anti-clockwise direction. A point and it’s image are always the same distance from the centre of rotation. The centre of rotation is the only invariant point. B ¼ turn clockwise = C 90º clockwise A D’ D B’ C’ ¼ Turn anti-clockwise = 90º Anti-clockwise C’ B C B’ A The line equidistant from an Mirror line object and its image Centre of rotation The point an object is rotated Invariant about Doesn’t change What is invariant in Reflection rotation The mirror line Centre of rotation By what angle is this flag rotated about point C ? C 180º Remember: Rotation is always measured in the anti clockwise direc By what angle is this flag rotated about point C ? C 90º By what angle is this flag rotated about point C ? C 270º Ex 26.07 Page 411 Qn 1, 2, 3, 7 and 8. Ex 26.08 Page 412 Qn 1, 3, 4 and 6. 1 D C’ B’ D’ A’ A C B A’ C’ C 2 B’ A B C D 3 B’ C’ A A’ D B C D’ 7 A C’ D’ B B’ A’ s s 8 1. a) P b) R c) QS 3. 180° 4. 0° or 360° 8. a) R b) Q c) CB A figure has rotational symmetry about a point if there is a rotation other than 360° when the figure can turn onto itself. Order of rotational symmetry is the number of times a figure can map onto itself. Order of rotational symmetry= 4 Order of rotational symmetry= 3 A shape has line symmetry if it reflects or folds onto itself. The fold is called an axis of symmetry. Line symmetry= 2 The number of axes of symmetry plus the order of rotational symmetry. 2+2=4 8 7 6 5 -4 -3 2 1 0 1 2 3 4 5 6 7 8 7 8 1. Move the red dot by the following values and state where it now lies. (-1), (4), (7), (-4) and (11). 8 7 6 5 -4 -3 2 1 0 1 2 3 4 5 6 1. Move the green dot by the following values and state where it now lies. (-6), (3), (-9), (-4) and (5). Group One- Kelly, Ruby, Bella, Chrisanna and Bianca Group Two- Hannah B, Grace, Shanice, Grace and Georgia R Group Three- Hannah C, Remy, Olivia, Kendyl and Sarah Group Four- Kelsey, Shaquille, Kiriana, Cadyne and Claudia Group Five- Lauran, Ashlee, Sophie, Georgia W and Emily S Group Six- Esther, Emily M, Jemma, Amelia and Julia Each point moves the same distance in the same direction There are no invariant points in a translation (every point moves) • Vectors describe movement + + - () x y - ← movement in the x direction (right and left) ← movement in the y direction (up and down) Vectors describe movement Each vertex of shape EFGH moves along the vector () -3 -6 To become the translated shape E’F’G’H’ Translate the shape ABCDEF by the vector to give the image A`B`C`D`E`F`. () -4 -2 -5 +4 +2 -6 +3 +4 -6 -2