1. Find another five letter word whose letters each belong in different categories. I’ve divided the alphabet into five categories as shown below. Can you identify the category to which each letter of the word BRA I N belongs? Give a brief explanation for your choice. (1) M T U V W Y (2) C D E K (3) S Z (4) H O X (5) F G J L P Q I’ve divided the alphabet into five categories as shown below. Can you identify the category to which each letter of the word BR A I N belongs?

2. Midterm Exam 24 students took the midterm Mean = 120/150 = 80% Median = 133.5/150 = 89%

19. f) True or False: The measure of  DEC is equal to the sum of the measures of  DAC and  DCE. Justify your answer.

20. 180° rotational symmetry Vertical line symmetry Horizontal line symmetry Horizontal and vertical line symmetry, and 180° rotational symmetry No symmetry Find another five letter word whose letters each belong in different categories. I’ve divided the alphabet into five categories as shown below. Can you identify the category to which each letter of the word BRA I N belongs? Give a brief explanation for your choice. (1) M T U V W Y (2) C D E K (3) S Z (4) H O X (5) F G J L P Q I’ve divided the alphabet into five categories as shown below. Can you identify the category to which each letter of the word BR A I N belongs? B R A I N

21. Transformations Reflections Rotations Translations Dilations These transformations are isometries. An isometry is a transformation in which the original figure and its image are congruent. Thus isometries preserve distance and angle measure.

22. If A is the reflection image of point A over line l, then l is the perpendicular bisector of line segment AA Reflections A A l

23. The Burning House Problem A man is walking in an open field some distance from his house. It’s a beautiful day and he is carrying an empty bucket with him to collect berries. Before long, he turns around and, to his horror, sees that his house in on fire. Without wasting a moment, he runs to a nearby river (which runs in a straight line from east to west) to fill the bucket with water so that he can run to his house to throw water on the fire. Naturally, he wants to do this as quickly as possible. Describe how to construct the point on the river bank to which he should run in order to minimize his total running distance (and time).

24.   M H   M

25.   M H   M  Q

26. B On a billiard table, a player must hit ball A into pocket B without touching the other three balls shown. Where should the player aim?

27. Reflection image of point A. B

28. Reflection image of point B. B

29. B

30. B

32. Using Geometer’s Sketchpad, construct a rhombus (not a square) by using only the 2 basic draw tools (point and line segment) and reflections. The figure should remain a rhombus when points are dragged.

34. Regular Polygon – A polygon with all sides congruent and all angles congruent. Measure of each central angle = Number of diagonals = Measure of each interior angle = Sum of the interior angles = 140  40  Every regular polygon can be inscribed in a circle.

35. Rotations Use Geometer’s Sketchpad to construct a regular nonagon.

36. Use Geometer’s Sketchpad to construct an angle ABC near the left side of the screen. Construct a line segment DE somewhere else on the screen. Use Sketchpad to construct an angle congruent to  BAC and having segment DE as one of its sides. Rotations

37. Use Sketchpad to construct a triangle congruent to ABC and having point P as one of its vertices. Translations Use Geometer’s Sketchpad to construct an acute triangle ABC near the lower left of the screen. Construct point P in the center of your screen. - Often called glide or slide transformations

38. HW problem 1: Use Geometer’s Sketchpad to construct a rectangle whose side lengths are in the ratio of 2:1 without using the perpendicular, parallel, or midpoint options in the construct menu, and without constructing any circles. Construct the letter A using Geometer’s Sketchpad. Your A must be perfectly vertical and symmetric. In other words, it cannot look like this or this. A HW Problem 3: Construct a line segment AB using Geometer’s Sketchpad. Without changing line segment AB in any way, construct a rhombus (not a square) so that AB is one diagonal of the rhombus. HW Problem 2: If you don’t complete these in class, complete as part of tonight’s homework.