PH #5.5 Triangle Inequalities

• (1, 2, 3,5, 7, 11, 13)
• (17-27) odd
• (32)
• (42-47) all

5.3 (this is a pdf file on my website!)

• (6-18) all

PH #3.3

• (7-11) odd
• (31-35) odd
• (43)
• (64-67) all

PH #3.4

• (21, 23, 47, 48, 64-66)

#5.1 Triangle Sum (pdf file on website)

• (7-8)

#5.2 Properties of Isosceles Triangles (pdf fileo n website)

• (4-7) all

#6.1 Polygon Sum (pdf file on website)

• (1-13) all

PH #2.5 Angle Relationships (you guys know how much i "love" this book!)

• (20-22) all
• (29-30) all
• (39-42) all
• (47-54) all
• (57-65) all
• Bascially, you will always be responsible for doing the sections with the subtitle "Algebra" as well as the FCAT Practice section

PH #3.1 Properties of Parallel Lines

• (14-16) all
• (23-25) all
• (37-41) all

4.2 problems

• this is a PDF file on my website underneath the Worksheets section
• for this one time only, you can click on the link below to get it, but be sure you can find it on the website as well!
• http://msichan.com/Documents/4.2%20problems%20gh.pdf
• (1-7, 9)

Happy Yom Kippur to all of my Jewish students! Have a nice, long, PG-13 weekend everyone!

Polygon Sum Conjecture

1. Draw a triangle. Use a protractor to measure each angle. Find the sum of all the angles.
2. Draw a quadrilateral. Use a protractor to measure each angle. Find the sum of all the angles.
3. Draw a pentagon. Use a protractor to measure each angle. Find the sum of all the angles.
4. Draw a hexagon. Use a protractor to measure each angle. Find the sum of all the angles.
5. Draw a heptagon. Use a protractor to measure each angle. Find the sum of all the angles.
6. Draw an octagon. Use a protractor to measure each angle. Find the sum of all the angles.

Complete the following chart:

# of sides: 3 4 5 6 7 8 n

# of triangles formed:

Sum of all the angles:

Constructions

Construct the 3 perpendicular bisectors of:

1. an acute triangle
2. an obtuse triangle
3. a right triangle

Now construct the circumscribed circles of each of the above triangles.

Construct the 3 angle bisectors of:

4. an acute triangle

5. an obtuse triangle

6. a right triangle

The 3 angle bisectors of a triangle intersect at one point callede the incenter.

For numbers 4-6, pick the longest side of each triangle. Use your knowledge of how to construct a perpendicular through a point NOT on the line to construct a perpendicular to your longest side through the incenter.

Good luck! See you tomorrow! Remember, tomorrow is early release which means we end at 12:40.

P.S. make sure you KNOW the definitions for median and altitude BEFORE you walk into my class tomorrow. I do not have time for you to be confused! KNOW them like the back of your hand!

Constructing Perpendiculars &Different Types of Angles
(For those of you who have been absent or need extra help, go to hstutorials.net (thanks, Taylor!), click on Geometric Constructions to view video explanations)

1. On the top half of your paper, construct a perpendicular line through a point NOT on the line.
2. On the bottom half of your paper, construct a perpendicular through a point ON the line.
3. On the top half of the back side, draw a segment. Label it AB. Now construct perpendicular bisectors to divide it into 4 congruent parts.
4. On the bottom half of the back side, draw a line segment so close to the edge of the paper that you can only swing arcs on one side of the segment. Now construct the perpendicular bisector of the segment.
5. On the top half of a second sheet of paper, construct a 60 degree angle.
6. On the bottom half of the second sheet of paper, construct a 45 degree angle. Using the 45 degree angle you just constructed, construct a 22 1/2 (twenty-two and a half) degree angle.
7. On the top half of the back side of the second sheet of paper, construct a 30 degree angle. Using the 30 degree angle you just constructed, construct a 15 degree angle.
8. On the bottom half of the back side of the second sheet of paper, construct a 120 degree angle.
9. On the top half of the 3rd sheet of paper, construct a 75 degree angle.
10. On the bottom half of the 3rd sheet of paper, construct a 52 1/2 degree (fifty-two and a half) angle.
11. On the top half of the back side of the 3rd sheet of paper, construct a 135 degree angle.
12. On the bottom half of the back side of the 3rd sheet of paper, construct a 105 degree angle.

Tomorrow's constructions are going to be a bit confusing. To make them easier, bring in computer paper and colored pencils for tomorrow's constructions. Of course, these are just suggestions and not mandatory. I'm just trying to make it easier for you.

Constructions

1. Draw an acute angle on the top half of your paper. Duplicate it.
2. Draw an obtuse angle on the bottom half of your paper. Duplicate it.
3. On the back of your paper, (top half), draw an acute angle. Label it angle A. Now draw another acute angle next to it. Label it angle B. Construct a third angle so that it is congruent to angle A + angle B.
4. On a new sheet of paper (top half), construct a perpendicular bisector.
5. On the bottom half, draw an angle. Label it angle D. Bisect it.
6. On the back side (top half), draw an obtuse angle. Label it angle E. Bisect it.
7. On the bottom half, draw a line segment. Label it AB. Draw another segment of a diffrent length. Label it CD. Now construct a new segment so that it is equal in length to AB +CD.

Be sure to have your compass and straightedge with you on Monday!!!!!

We will be learning how to do constructions next week. If you would like to get a head start on these lessons (HIGHLY RECOMMENDED), you can try googling "constructions". We will be learning how to "duplicate a line segment", "duplicate an angle", "bisect a segment", "bisect an angle", "construct a perpendicular line through a point ON the line", "construct a perpendicular line through a point NOT on the line" and "construct parallel lines". If you can find a video showing you how to do it, even better. If you find a good website that SHOWS you how to do any of these constructions, write it down and bring it to share with your colleagues. Everyone should have at least 5 websites to share on Monday.

Vocabulary Quiz on Monday! Use your index cards to study, study, study this weekend!!!!!

True or False?

The following exercises will help you visualize relationships between geometric figures in a plane and in space. Determine whether the following statements are true or false. Make a sketch or use physical objects to demonstrate each true statement. For each false statement, produce a counterexample illustrating that each is false. If you wish to create physical models, use pencil tips and thumbtacks to represent points. Use rulers, pencils, or stiff wires to represent lines. Use a piece of paper or cardboard to represent planes. Some of these can be challenging I know which is why I am asking you to make a PHYSICAL model to help you visualize the statement.

1. For every line segment, there is exactly one midpoint.
2. For every angle, there is exactly one angle bisector.
3. If two different lines intersect, then they intersect at one and only one point.
4. If 2 different circles intersect, then they intersect at one and only one point.
5. There is exactly one and only one line perpendicular to a given line through a given point on the given line.
6. In a plane, there is exactly one line perpendicular to a given line through a given point on the given line.
7. There is exactly one line perpendicular to a given line through a given point NOT on the given line.
8. In every triangle, there is exactly one right angle.
9. Through a given point NOT on a given line, there is one and only one line that can be constructed parallel to the given line.
10. It is possible for 2 triangles to intersect in one point, 2 points, 3 points, 4 points, 5 points, or 6 points, but not exactly 7 points.
11. One and only one distinct line can be drawn through 2 different points.
12. One and only one distinct plane can be made to pass through 3 NONcollinear points.
13. Exactly one disitinct plane passes through one line and a point NOT on the line.
14. If a line intersects a plane NOT containing it, then the intersection is exactly one point.
15. If 2 lines are perpendicular to the SAME line, then they are parallel.
16. If 2 different planes intersect, then their intersection is a line.
17. If a line and a plane have NO points in common, then they are parallel.
18. If 2 coplanar lines are BOTH PERPENDICULAR to a third line in the SAME plane, then the 2 lines are parallel.
19. If 2 different planes do NOT intersect, then they are parallel.
20. If a plane intersects 2 parallel planes, then the LINES OF INTERSECTION are parallel.
21. If 3 RANDOM planes intersect (no 2 planes are parallel and no 3 through the same line), then they divide space into 6 parts.
22. If a line is perpendicular to 2 lines in a plane, but the lines is NOT contained in the plane, then the line is perpendicular to the plane.
23. If 2 lines are perpendicular to the same plane, then they are parallel to each other.

Vocabulary

• create vocabulary index cards
• you may use 3x5 index cards or 4x6 index cards. your choice.
• on one side of the card, write the vocabulary word
• on the other side of the card, write the definition AND draw a picture illustrating the word you're trying to define

1. point
2. line
3. plane
4. collinear
5. coplanar
6. space
7. line segment
8. ray
9. angle
10. congruent
11. counterexample
12. right angle
13. acute angle
14. obtuse angle
15. midpoint
16. angle bisector
17. parallel
18. perpendicular
19. complementary
20. supplementary
21. vertical angles
22. linear pair
23. polygon
24. convex
25. concave
26. triangle
27. quadrilateral
28. pentagon
29. hexagon
30. consecutive vertices
31. consecutive angles
32. consecutive sides
33. perimeter
34. diagonal
35. equilateral
36. equiangular
37. regular polygon
38. right triangle
39. acute triangle
40. obtuse triangle
41. scalene
42. isosceles
43. median
44. altitude
45. trapezoid
46. kite
47. parallelogram
48. rhombus
49. rectangle
50. square

This may seem like a lot of words to you, but if you take 50 vocabulary words and divide it by the 4 nights (Friday night, Saturday night, Sunday night, and Monday night) you have to complete this assignent, it gives you an average of 12.5 words per evening. This is definitely doable.

PH #1.1

• FCAT Practice (56-59) all

PH #1.2

• read pgs. 10-13
• take notes. pay particular attention to vocabulary words Highlighted in yellow, as well as, examples 1, 2, 3, and 4
• FCAT Practice (85-89) all

PH #1.3

• read pgs. 17-19
• take notes. pay particular attention to vocabulary words highlighted in yellow, as well as, examples 1, 2, and 3
• FCAT Practice (63-70) all

FACTORING

Factor the following trinomials: the symbol ^ means "raised to". For instance, 5x^4 means 5 times x raised to the fourth power

1. 3x^2+5x+20
2. x^2+10x+24
3. x^2-14x+33
4. x^2+3x-28
5. 6x^2-31x+35
6. 6x^2+11x-35
7. 2^2+11x+12
8. 4x^2+7x+3
9. 2x^2-7x+6
10. 3x^2-16x+5

If you didn't finish last night's #1.6 problems, you have another night to complete it.

#1.6 Mathematical Modeling
Draw pictures for yourselves to model each situation. Use points to represent people and line segments to represent connections such as a handshake or a conversation.

1. How many diagonals can you draw from ONE vertex in a polygon with 35 sides?
2. If you place 35 points on a piece of paper so that NO THREE are in a line, how many line segments are necessary to connect each point to all the others?
3. What's the TOTAL number of diagonals in a 35 sided figure?
4. If you draw 35 lines on a piece of paper so that no 2 lines are parallel to each other and no three pass through the same point, how many times will they intersect?
5. Is there a geometrical relationship between the first 4 problems?
6. If there are 20 ppl sitting around a table, how many different pairs of ppl can have conversations during dinner?
7. If 40 houses in a community all had to have direct lines to one another in order to have telephone service, how many lines would be necessary? Would it be practical? Is there a more practical alternative?
8. If each team in a 10 team league plays each of the other teams four times in a season, how many league games are played during one season? What geometric figures can you use to model teams and games played?
9. Each person at a dinner table shakes hands with everyone EXCEPT the 2 ppl on either side of him (this means he won't shake hands with either the person directly to his left and the person directly to his right). How many handshakes will there be among 20 diners?
10. A polygon has six diagonals leaving each vertex. How many sides does it have?
11. A polygon has 90 diagonals. How many sides does it have?
12. Each person at a party shook hands with everyone else exactly once. There were 66 handshakes. How many ppl were at the party?
13. Find the nth term: 1, 6, 15, 28, 45, 66
14. Find the nth term: 4, 7, 10, 13, 16, 19
15. Find the nth term: -4, 3, 16, 35, 60, 91
16. Find the nth termL -1, 0, 9, 26, 51, 84
17. 33+35+37+...+351=?
18. 48+50+52+...+688=?
19. 45+46+47+...+986=?
20. Find the next term in the sequence: 1, 246, 546, 909, 1344, 1861