Geometry Unit 5: Understanding Angles and Transformations

1. Session 55 Draw six segments that pass through every dot in the figure without taking your pencil off the paper.

2. Go over test

3. Unit 5 Vocabulary

4. Angle • An angle measuring less than 90° but greater than 0° The angle is

5. Circle • The set of points on a plane at a certain distance, or radius, from a single point, the center

6. Perpendicular Line Two lines that intersect at a right angle (90°). Written as

7. Parallel Line Lines in a plane that either do not share any points and never intersect, or share all points. Written as

8. Line Segment A line with two endpoints. Written as

9. Point An exact position or location in a given plane. Point A or Point B

10. Line The set of points between points P and Q in a plane and the infinite number of points that continue beyond the points. Written as

11. Distance along a line The linear distance between two points on a given line.

12. Right Angle An angle that measures 90°.

13. Acute Angle An angle measuring less than 90° but greater than 0°.

14. Obtuse Angle An angle measuring greater than 90° but less than 180°.

15. One-to-One A relationship wherein each point in a set of points is mapped to exactly one other point.

16. Pre-image The original figure before undergoing a transformation.

17. Image The new, resulting figure after a transformation

18. Isometry A transformation in which the preimage and image are congruent.

19. Transformations are called RIGID if every image is congruent to its preimage. Rigid transformations can also be referred to as an ISOMETRY. Every segment is congruent to its image.

20. Which of the following are rigid transformations? (Isometry)

21. Isometries not onlypreserve lengths, butthey preserve angle measuresparallel lines, andbetweenness of points

22. Find the value of each variable, given that the transformation is an isometry.

23. Congruent Figures are congruent if they have the same shape, size, lines, and angles.

24. Similar Triangles Triangles are similar if they have the same shape but have different sizes.

25. Even and Odd Functions

26. Algebraically A function is even if All of the exponents of the variable are even. A function is odd if All of the exponents of the variable are odd. A function is neither if The exponents are a mixture of odd and even

27. BEWARE OF CONSTANTS All constants really have a x0

28. x0 is EVEN!!

29. Graphically A function is even if The graph reflects across the y-axis (means you can fold it hotdog style and it would match up). A function is odd if The graph has 180 rotational symmetry about the ORIGIN (means you could turn it upside-down & it would still look the same...it must go through the origin).

30. Even, Odd or Neither? Ex. 1 Algebraically 1 ODD

31. Even, Odd or Neither? Ex. 2 Algebraically x0 EVEN

32. Even, Odd or Neither? Ex. 3 Graphically EVEN

33. Even, Odd or Neither? Ex. 4 Graphically Neither 

34. Even, Odd or Neither? 1 x0 EVEN ODD

35. Even, Odd or Neither? x0 ODD ODD Even

36. Even, Odd or Neither? 1 1 x0 neither ODD neither

37. Even, Odd or Neither?  EVEN ODD

38. Even, Odd or Neither?   EVEN Neither ODD

39. If the dots shown are part of an even function, what points are also on the function?

40. If the dots shown are part of an odd function, what points are also on the function?

41. HWPractice WS