Perry High School. Geometry: S2W6

Transcription

1 Geometry: S2W6 Monday: 7.1 Rigid Motion in a Plane Pre-reading due Tuesday: 7.1 Work Day Wednesday: 7.2 Reflections Pre-reading due Thursday: 7.2 Work Day Friday: 7.3 Rotations Pre-reading due Next Week: Start Chapter 7.3, 7.4, 7.5, 7.6 1

2 Body Scan Meditation Skill Review Rigid Motion in a Plane Study Guide p. 394 Key Vocabulary Distance Formula (1-3) Complete the Statement (4-9) Study Strategy 2

3 7.1 Lecture Chapter 7: Movement in a Plane Art, animation, branding, etc. 7.1: Ridged Motion in a Plane Identifying Transformations Using Transformations in Real Life 3

4 MC Escher: Day and Night 4

5 Definitions Preimage a figure in a plan that can be reflected, rotated, or translated - starting object, blue Image the aftermath of a figure in a plan that has been reflected, rotated, or translated ending object, red Transformation the operation that MAPS, or moves, the preimage onto the image. 5

6 Preimage and Image 6

7 3 Basic Transformations 7

8 Transformation: Rotation 8

9 Transformation: Reflection 9

10 Transformation: Translation 10

11 Isometry a transformation that preserves lengths, angle measures, parallel lines, and distances between points. Isometry Isometric Paper? 11

12 Isometric Circles 12

13 In Architecture 13

14 In Architecture 14

15 More in arch. 15

16 Rotational Symmetry /search?q=rotational+ symmetry&espv=2&bi w=1221&bih=818&so urce=lnms&tbm=isch &sa=x&ei=x4dsvj_ MHoamyAS0gIGIAw& ved=0cayq_auoaq #tbm=isch&q=rotation al+symmetry+logos&r evid= Popular with Logos, Branding, Marketing, Identification, etc. 16

17 Day 1 Work: Mixed Review, page 402: : Day 1 & 2 m/watch?v=wfuv_8lo HD4 (15 minutes) Work: Guided Practice, page 399: 1-11 Day 2 p399: 12-42, 44, 45 Board Check 17

18 7.2 Meditation Pre-Reading Due Focus on Reflections Using reflections in a plane Reflections with a line of symmetry 18

19 Reflections and Line of Reflections A reflection over a line m is a transformation that maps every point P in the plane to a point P, so that the following properties are true: 1. If P is not on m, then m is the perpendicular bisector of segment PP 2. If P is on m, then P=P. 19

20 Reflection: Basic 20

21 Reflection: Coordinate Plane If (x,y) is reflected over the x-axis, its image is the point (x,-y). If (x,y) is reflected over the y-axis, its image is the point (-x,y). 21

22 Reflection: x-axis 22

23 Reflection: y-axis? 23

24 Theorem A reflection is an isometry 24

25 Line of Symmetry A figure in the plane has a line of symmetry if the figure can be mapped onto itself by a reflection in the line. 25

26 Lines of Symmetry: Ex 26

27 More Lines of Symmetry 27

28 7.2: Day 1 & 2 Day 1 Mixed Review, page 410: Guided Practice, page 407: 1-14 Day 2 Check D1 7.2: 15-32, 36-41, Board Presentation 28

29 Rotations 29

30 Using Rotations: Definitions Rotation a transformation in which a figure is turned about a fixed point. Center of Rotation the fixed point about which a rotation transformation is turned. Angle of Rotation rays drawn from the center of rotation to a point and its image for this angle. 30

31 Center of Rotation 31

32 Angle of Rotation 32

33 Rotation: Properties A rotation about a point P through x degrees (x o ) is a transformation that maps every point Q in the same plane to a point Q, so that the following properties are true: 1. If Q is not point P, then QP = Q P and m QPQ =x o 2. If Q is point P, then Q=Q 33

34 Rotation Theorem A Rotation is an Isometry 34

35 Rules for Rotation around (o,o) Counter-Clockwise! Rotate 90 o, P(x,y) P (-y,x) Rotate 180 o, P(x,y) P (-x,-y) Rotate 270 o, P(x,y) P (y,-x) Example: A quadrilateral has verticies Q(4,0), R(4,3), and S(2,4). P(3,-1), Rotate PQRS 180 o counterclockwise about (0,0) and name the coordinates of the image. 35

36 Theorem 7.3 If lines k and m intersect at point P, then a reflection over k followed by a reflection over m is a rotation about point P. The angle of rotation is 2x o, where x o is the measure of the acute or right angle formed by k and m. M BPB = 2x o 36

37 2 Reflections = 1 Rotation 37

38 Rotational Symmetry Rotational Symmetry a figure in a plane has rotational symmetry if the figure can be mapped onto itself by a rotation of 180 o or less. 38

39 Rotational Symmetry 39

40 7.3: Day 1 & 2 Day 1 Work: Mixed Review page 419: Work: Guided Practice page 416: 1-12 Day 2 Check D1 7.3: , 22-30, 31 43, 45 54; Quiz 1: 1 8 Board Presentation 40