1. CONFIDENTIAL1 Good Afternoon! Today we will be learning about Similarity and Symmetry Let’s warm up : Write Reflection, Rotation or Translation to describe how the figure was moved: 1)2) 3) 4) 1) Reflection, Translation 2) Rotation 3) Rotation 4) Reflection

2. CONFIDENTIAL 2 If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called Congruent: The three main Transformations are:  Reflection : Flip!  Rotation : Turn!  Translation : Slide! After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths. Let’s review what we did in the last session We learnt about transformation.

3. CONFIDENTIAL 3 The central line is called the Mirror Line, and it doesn't matter what direction the mirror line goes, the reflected image is always the same size, it just faces the other way. A reflection over a line, is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side. Reflection Review

4. CONFIDENTIAL 4 You can try reflecting different shapes about different mirror lines. Just approach it step-by-step. For each corner of the shape: Measure from the point to the mirror line (must hit the mirror line at a right angle) Step1 Reflection Review

5. CONFIDENTIAL 5 Measure the same distance again on the other side and place a dot. Then connect the new dots up! Step2 Step3 Reflection Review

6. CONFIDENTIAL 6 It is common to label each corner with letters, and to use a little dash (called a Prime) to mark each corner of the reflected image. Here the original is ABC and the reflected image is A'B'C' Labels Review

7. CONFIDENTIAL 7 Rotation When we "rotate" an object round a point. The distance from the center to any point on the shape stays the same! and Every point makes a circle around the center.! We can notice that "Rotation" means turning around a center. Review

8. CONFIDENTIAL 8 A rotation is a transformation, that moves every point around a fixed point (usually the origin). Rotation A rotation creates a figure that is congruent to the original figure and preserves distance and orientation. Review

9. CONFIDENTIAL 9 Review Translation In Geometry, "Translation" simply means Moving.. without rotating, resizing or anything else, just moving. Every point of the shape must move: * the same distance * in the same direction. A translation is a transformation that slides every point of a figure the same distance in the same direction.

10. CONFIDENTIAL 10 Let’s start with Similarity and Symmetry Similar: Two shapes are Similar if the only difference is size. If one shape can become another using Resizing, then the shapes are Similar. Example: When two shapes are similar, then:  corresponding angles are equal, and  the lines are in proportion.

11. CONFIDENTIAL 11 Resized Resized and Reflected Resized and Rotated These shapes are all Similar. Sometimes it can be hard to see if two shapes are Similar, because you may need to turn, flip or slide one shape as well as resizing it. If one shape can become another using Resizing, then the shapes are Similar.

12. CONFIDENTIAL 12 Fold this picture in half. The two parts match exactly. This picture has “symmetry.” Where you fold the shape, or the fold line, is called the line of symmetry. Line of symmetry Symmetry: When a picture or figure has symmetry, it can be folded in half so that the two parts match exactly.

13. CONFIDENTIAL 13 Line Symmetry A figure has line symmetry if it can be folded in half so that the two halves match exactly i.e. one half of it is the mirror image of the other half. Line symmetry is also called bilateral symmetry.

14. CONFIDENTIAL 14 Figures can have any number of lines of symmetry, from no lines of symmetry to an infinite, or unlimited, number of lines of symmetry. No lines of symmetry One line of symmetry Two lines of symmetry Infinite lines of symmetry The Line Symmetry is sometimes called Reflection Symmetry or Mirror Symmetry.

15. CONFIDENTIAL 15 Rotational Symmetry With rotational Symmetry, the shape or image can be rotated clockwise or counterclockwise 180°and it still looks the same. Rotational Symmetry: A figure has rotational symmetry if it can be rotated about a point less than a full turn to make the figure look the same as it did before the rotation. Quarter turn Half turn 3-Quarter turn

16. CONFIDENTIAL 16 Point Symmetry Point Symmetry: is when every part has a matching part. * the same distance from the central point * but in the opposite direction. Point Symmetry is sometimes called Origin Symmetry, because the "Origin" is the central point about which the shape is symmetrical.

17. CONFIDENTIAL 17 Same from Opposite Direction? Yes, pick a direction, and anything with Point Symmetry will look the same from the opposite direction, too. These Letters have Point Symmetry, too! It looks the same Upside Down! (... or from any two opposite directions*)

18. CONFIDENTIAL 18 Symmetry exists all around us You can find symmetry in nature, architecture and art.

19. CONFIDENTIAL 19 BREAK

20. CONFIDENTIAL 20 GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/kids- jigsaw-puzzles/12-piece-jigsaw/11-07-06- snowprincess.html

21. CONFIDENTIAL 21 Assignments Write whether of figures are similar or not: 1) 2) 3) 4) 5) 2) Not Similar 1) Similar 3) Similar 4) Not Similar 5) Similar

22. CONFIDENTIAL 22 Is the dotted line a line of symmetry: 6) 8) 7) 9) 10) 6) yes 7) no 8) yes 9) yes10) no

23. CONFIDENTIAL 23 Very Good! Let's Review Similar: Two shapes are Similar if the only difference is size. If one shape can become another using Resizing, then the shapes are Similar. Example: When two shapes are similar, then:  corresponding angles are equal, and  the lines are in proportion.

24. CONFIDENTIAL 24 Review Resized Resized and Reflected Resized and Rotated These shapes are all Similar. Sometimes it can be hard to see if two shapes are Similar, because you may need to turn, flip or slide one shape as well as resizing it. If one shape can become another using Resizing, then the shapes are Similar.

25. CONFIDENTIAL 25 Review Fold this picture in half. The two parts match exactly. This picture has “symmetry.” Where you fold the shape, or the fold line, is called the line of symmetry. Line of symmetry Symmetry: When a picture or figure has symmetry, it can be folded in half so that the two parts match exactly.

26. CONFIDENTIAL 26 Review Line Symmetry A figure has line symmetry if it can be folded in half so that the two halves match exactly i.e. one half of it is the mirror image of the other half. Line symmetry is also called bilateral symmetry.

27. CONFIDENTIAL 27 Review Figures can have any number of lines of symmetry, from no lines of symmetry to an infinite, or unlimited, number of lines of symmetry. No lines of symmetry One line of symmetry Two lines of symmetry Infinite lines of symmetry The Line Symmetry is sometimes called Reflection Symmetry or Mirror Symmetry.

28. CONFIDENTIAL 28 Review Rotational Symmetry With rotational Symmetry, the shape or image can be rotated clockwise or counterclockwise 180°and it still looks the same. Rotational Symmetry: A figure has rotational symmetry if it can be rotated about a point less than a full turn to make the figure look the same as it did before the rotation. Quarter turn Half turn 3-Quarter turn

29. CONFIDENTIAL 29 Review Point Symmetry Point Symmetry: is when every part has a matching part. * the same distance from the central point * but in the opposite direction. Point Symmetry is sometimes called Origin Symmetry, because the "Origin" is the central point about which the shape is symmetrical.

30. CONFIDENTIAL 30 Review Same from Opposite Direction? Yes, pick a direction, and anything with Point Symmetry will look the same from the opposite direction, too. These Letters have Point Symmetry, too! It looks the same Upside Down! (... or from any two opposite directions*)

31. CONFIDENTIAL 31 Symmetry exists all around us You can find symmetry in nature, architecture and art. Review

32. CONFIDENTIAL 32 You have done a nice job. See you in the next session.