Geometry; 5/31

We went over the homework from last week that dealt with compositions of functions to start the period.  We then introduced the new concepts of inverses and identities when it comes to geometric transformations.  We went over a few examples for each transformation and then reminded the students of how inverses and identities work with algebra. The students got started on their assignment towards the end of the period.

Assignment:  page 607;  CE  #11-19;  page 607-608;  WE  #1-26 all

Honors Geometry; 5/31

We spent the first part of the period going over the constructions review packet from last week.  We then went through the last section of chapter 10 that we will cover.  It involved constructing special segments that divide other segments up evenly or into proportional lengths.  We reviewed what a geometric mean is and how to construct one.  We also worked more with constructing parallel lines to divide up segments proportionally.  The students then got started on their assignment.

Assignment:  section 10-5;  page 399;  WE  #1-10

Geometry; 5/26

We discussed our next topic involving transformations today by taking a look at compositions both in algebra and geometry.  We reviewed what a function was and how to work with compositions of functions.  We then did the same thing with compositions of transformations in geometry.  The key concept of how to read the notation and what order to perform the transformations in was demonstrated by 3-4 examples.  The students then got started on their assignment.


Assignment:  section 14-5 WS  (skip #6, 12, 24);    page 602;  CE  1-8;  page 603-604;  WE 5-11

Honors Geometry; 5/26

We went over our homework together and answered any questions that the students had.  We then mapped out the schedule for the last two weeks in terms of when the chapter 10 test would be and how the finals reviews and finals schedule would work.  We then started on a constructions packet that the students will have as their assignment over the weekend.

Assignment:  constructions packet

Geometry; 5/25

We spent the first part of the period going over homework and answering any questions that students had about rotations.  The lesson topic today focused on how to work with dilations in figures.  We talked about the connection to similarity that dilations have, and also the need for a scale factor in working with dilations.  We did 4-5 examples together of what dilations look like before students got started on their assignment.


Assignment:   section 14-5;  page 595;  CE  #1-6;    page 596;  WE  #1-14  (skip #7, 8)

Honors Geometry; 5/25

Due to the SBAC testing schedule, there was no class today.

Assignment:  none

Geometry; 5/24

Due to the SBAC testing schedule today, the geometry class period did not meet.

Assignment:  none

Honors Geometry; 5/24

We continued our work with constructions today by demonstrating how to construct circles and their respective tangent lines.  We also reminded the students how to inscribe and circumscribe circles around triangles.  After going through 4-5 examples together, the students got started on their assignment.


Assignment:  section 10-4;  page 395;  WE  #1-15

Geometry; 5/23

We continued our work with transformations today by going over how rotations work.  We went over the basic concepts of rotations and how the direction and amount of rotation are communicated.  We then went through 2-3 examples of how to graph rotations using the three rotation rules we developed.  The students then got started on their homework assignment.

Assignment:  rotation worksheet  (skip #13, 17, 18)  + page 590  WE  6-22 all  (skip #9, 10)

Honors Geometry; 5/23

We continued our work with concurrent lines and constructions today by taking a look at perpendicular bisectors and altitudes in triangles.  We went over 3 constructions together before filling out a summary page for the concurrent lines.  The students then got started on their homework assignment towards the end of the period.

Assignment:  section 10-3;  page 388-389;  WE  #1-14 all

Geometry; 5/20

We worked on how to mentally figure our images and preimages today before going through an explanation of how to carry our glide-reflections.  We did a couple of examples together before getting started on the homework.


Assignment:  section 14-3 worksheet +  page 586;  WE  #1-8

Honors Geometry; 5/20

We went over homework today and then started the next section on concurrent lines.  We were able to talk about 2 of the 4 constructions in this section, so we will finish our work on Monday.  We did a few examples before getting started on the homework assignment.


Assignment:  Constructions and Concurrent Lines worksheet

Geometry; May 19

We continued our work with transformations today by going over the 4 different rules for reflections and how they can be used to shorten problems.  We also then explained the next type of transformation known as a translation.  This is also known as a glide or slide.  We went over a couple of examples in class before getting started on the assignment.


Assignment:  translations WS + page 580   WE  #7-14

Honors Geometry; 5/19

We continued our work with parallel and perpendicular lines today by going over how to construct various shapes.  We also reviewed what altitudes and medians were and how these can be constructed in triangles.  We went over a few shapes together before getting started on the assignment.


Assignment:  section 10-2;  page 384;  WE  13-24

Geometry; 5/18

We started our last chapter today on transformations in geometry.  We went over what a transformation was and how to work with the new notation.  The transformation that we went over today involved reflections over different types of lines.  We worked with horizontal, vertical, and diagonal lines.  The students then got started on their assignment.


Assignment:  Reflections worksheet

Honors Geometry; 5/18

Our topic today involved constructing perpendicular and parallel lines.  The perpendicular lines had 3 different methods that we went over, while the parallel line constructions had just two.  After several examples together, the students got started on their assignment.


Assignment:  section 10-2;  page 383;  WE  #1-12 all

Geometry; 5/17

We turned in the chapter 13 review assignment at the beginning of the period and then the students spent the period taking the chapter 13 test.  

Assignment:  extra credit puzzle option

Honors Geometry; 5/17

We went over how to correct constructions and answered any questions from the homework last night to begin the period.  The lesson today focused on adding and subtracting angles, working with how to construct triangles using the SSS, ASA, and SAS copying method, and also how to generate 60, 120, and 30 degrees angles.  The students got started on their assignment at the end of the period.


Assignment:  section 10-1;  page 378-379;  WE 1-24 ;  skip #16 and 22

Geometry; 5/16

We went over 4-5 review problems together to begin the period as the students got ready for the chapter 13 test tomorrow.  After taking a look at these review problems, the students then spent the rest of the period working on the review sheet.  The answers to the review sheet appear below.


Assignment:  Chapter 13 review sheet


Answers:

1.  5 radical 5
2.  (x-5)2 + y2 = 121
3.  radius = 13;  (x + 2)2 + (y + 4)2 = 169
4.  -11/2
5.  0/-17 = 0
6.  (7, 2)
7.  ( -2, -1/2)
8.  center of circle: (-2, 4);  radius = 7
9.  center of circle: (0, -6);  radius = 3
10.  B = (-3, 9)
11.  graph of rectangle on axes
12.  m = -1
13.  m = 1
14.  perpendicular lines;  slopes are negative reciprocals
15.  same midpoint;  (3/2, 1/2
16.  a.  plot two points and connect them with a vector
       b.  (7, -13)
       c.  radical 218;  or 14.8
17.  (6, -2)
18.  (-27, 58)
19.  (-1, -5)
20.  graph of line;  y = 2/3 x - 4
21.  graph of line;  y = -4;  horizontal line with y-intercept of -4
22.  y = -3/2 x + 4
23.  y = 5/6 x + 5
24.  y = 2x - 1
25.  y = -3/2 x - 2
26.  y = 1/2 x + 7
27.  diagonals of rectangle are equal to radical (a2 - b2);  since both diagonals have the same length, they must be congruent.

Honors Geometry; 5/16

We went over the chapter 14 quiz in class today before getting started with our final chapter of the year -- Constructions!    We went over some basic pointers of how to use a compass and straight edge today, specifically working with copying segments and angles.  We will continue constructing some specific segments, angles, and triangles tomorrow in class.


Assignment:  Basic constructions worksheet;  #1-6;  10, 11

Honors Geometry; 5/13

We collected the Chapter 14 reviews to begin the period before starting the test.  The students had the period to complete the chapter 14 test.  We will start chapter 10 on Monday, which means the students will need to have a compass to use.


Assignment:   Extra credit puzzle option

Geometry; 5/12

We introduced the final concept of chapter 13 today by talking about how to organize coordinate proofs.  The main emphasis of what we did today was to go over how to make an advantageous drawing for the proof so that the calculations are much easier.  We went over several different types of examples of how to do this before getting started on the assignment.  The students worked more with variables today and will get more work with actual numbers tomorrow.


Assignment:  section 13-8;  page 558;  CE  #1-6;  page 558-559;  WE  #1-8;  page 563;  self test 2;  #1-5

Honors Geometry; 5/12

We went over the first review sheet for the chapter 14 test to start off the class.  Several questions got answered as we went over the key concepts one more time together.  We also reviewed the chapter 14 vocabulary words one more time before getting started on the second review sheet.

Assignment:  Chapter 14 review #2

Chapter 14 test in class tomorrow;  both review #1 and #2 are due at the beginning of the period.


Test 56 answers

1.  false
2.  false
3.  true
4.  true
5.  false
6.  false
7.  true
8.  true
9.  a.  no    b.  each point is mapped, but each one does not have a unique partner, since several of the points are mapped to the number 3 over and over.
10.  see graph
11.  yes
12.  -1, -1
13.  see graph

Test 57 answers

1.  12;  2
2.  (5, 12);  ( -8, 7)
3.  (-2, 5)
4.  R around A, -240 degrees
5.  9
6.  (4, 1)
7.  true
8.  true
9.  true
10.  true
11.  false
12.  true
13.  false
14.  segment AB
15.  segment BC
16.  Q
17.  C
18.  D
19.  D
20.  C
21.  Q
22.  see graph
23.  see graph

Chapter 14.1 to 14.5 quiz

1.  (-y, x)
2.  (y, x)
3.  (x, -y)
4.  (-x, -y)
5.  (-x, y)
6.  (y, -x)
7.  (-y, -x)
8.  F
9.  T
10.  T
11.  F
12.  F
13.  T
14.  F
15.  T
16.  (18, 4)
17.  (2, 81)
18.  (x + 3, y - 4)
19.  (-y, -x)
20.  (-x, -y)
21.  (4, -8)
22.  B
23.  A
24.  B
25.  B
26.  A
27.  C
28.  A' (-4, 1)  B' (-2, 3)  C' (-2, 0)
29.  A' (-1, -4)  B' (-3, -2)  C' (0, -2)
30.  A' (-4, -1)  B' (-2, -3)  C' (-2, 0)
31.  A' (5, 0)  B' (3, 2)  C' (3, -1)
32.  A' (-1, 4)  B' (-3, 2)  C' (0, 2)
33.  A' (2, 1/2)  B' (1, 3/2)  C' (1, 0)
34.  A' (-4, 3)  B' (-2, 1)  C' (-2, 4)
35.  A' (6, 2)  B' (2, 6)  C' (2, 0)

Geometry; 5/11

We continued our work with line equations today by further working with parallel, perpendicular, horizontal, and vertical lines.  Being able to navigate between the three forms of lines was the skill that we were focusing on.  After 5-6 examples together, the students then began working on their assignment.


Assignment:  section 13-7 worksheet + page 551;  #19-29 odd

Honors Geometry; 5/11

We went over the homework on symmetry today before wrapping up the final aspects of some of the number patterns in symmetry.  The common pattern between lines of symmetry, point symmetry, and rotational symmetry is what we demonstrated with a few shapes before getting started on the first review for this particular chapter.  The students used the last part of the period to work on their chapter 14 review sheet.

Assignment:  Chapter 14 review #1

Geometry; 5/10

We continued working with line equations today, but without graphing them.  We introduced a new type of line equation:  the point-slope form of a line.  We went over several examples of how to work with this equation and convert it to the other forms of lines that we have studied before.  The students then got started on their assignment towards the last part of the period.

Assignment:  section 13-7;  page 555;  WE  #1-28 all;     answer #1-25 in the y = mx + b form;  answer #26-28 in the standard form;  Ax + By = C 

Honors Geometry; 5/10

We introduced the topic of symmetry today in various shapes and went over the 4-5 different types of symmetries that are present both in the plane and in space.  We also went through how a tessalation is made and some different examples of artists who have used tesselations in their work.  The students then got started on their assignment towards the end of the period.


Assignment:  section 14-8;  page 611;  CE  #1-12;  page 612-613;  WE  #1-9;  12-17, 21, 22

Geometry; 5/9

We continued working with line equations today by going through problems involving two equations at the same time.  This is an algebra review topic called systems of equations.  We solved the systems in two different ways:  the first by graphing and the second by elimination of a variable.  We went over each method in class with a few examples before the students got started on their assignment.


Assignment:  systems of equations by graphing WS  #1-8;  systems of equations by elimination WS  #1-23 odd

Honors Geometry; 5/9

We continued our study of transformations today by going over what the identity and inverse transformations refer to.  We used some previous algebra knowledge to review these terms, and then we applied them to how they work with geometric transformations.  We went through several mental examples dealing with various drawings before the students got started on their assignment.


Assignment:  section 14-7;  page 607-608;  CE  11-19;  WE  1-28

Honors Geometry; 5/6

We went over our quiz from chapter 14 today to start the period.  We then continued on in chapter 14 in dealing with composites of mappings.  These are situations in which two mappings are done right after the other.  The order is important, as the mappings will often produce different results.  The composites can be performed on both algebraic functions and geometric transformations.  We modeled 4-5 such examples together before getting started on the homework.


Assignment:  section 14-6;  page 603-604;  WE #1-24

Geometry; 5/5

We went over a few of the review problems today to begin the period and then turned in the chapter 13 review sheet.  The students then spent the rest of the period working on the chapter 13 quiz.


Assignment:  extra credit puzzle option

Honors Geometry; 5/5

We turned in our chapter 14 quiz review today at the beginning of the period.  The students then took the rest of the period to take the chapter 14 quiz.


Assignment:  extra credit puzzle option

Geometry; 5/4

We went over the homework together and then reviewed three different problems in preparation for the quiz tomorrow.  The students then spent the rest of the period working on their review sheet.


Assignment:  Chapter 13 quiz review

page 1 answers

7.  5
9.  13
11.  not on the same line
13.  (1, -3);  r = 4
15.  (-1, 10);  r = 5/3
17.  (x+1)2 + (y+2)2 = 9
19.  (x + 2)2 + y2 = 2
21.  slope of OA = 0;  slope of BC = 0;  slope of OC = 3/2;  slope of AB = 3/2;
      both pairs of opp. sides have the same slope, so the figure is a parallelogram

page 2 answers

1.  2/3
2.  8/5
3.  -1/2
4.  -1/3
5.  undefined
6.  -e/a
11.  3
12.  -8
13.  -1/3
14.  1/2
15.  1/2
16.  -2
17.  -4/3
18.  -4/3
19.  3/4
21.  slope of RS = 1/2;  slope of ST = -3/4;  slope of RT = -2
         RS is perpendicular to RT because their slopes are negative reciprocals
         perpendicular sides mean that a right angle is in the triangle

page 3 answers

4.  (-5, 1);  radical 26
6.  (-1, -2);  radical 5
8.  k = 8
10.  (-2, 7)
12.  (13, 7)
14.  (1, 2)
16.  (4.3, 4)
18.  (e + j / 2  ,  f + k / 2)
20.  10;  4/3;  (1, 1)
22.  (7, 10)
24.  (-5, 1)

Honors Geometry; 5/4

We went over the homework and spent some time going through a few review problems together before working on the chapter 14 quiz review today in class.  Tomorrow is the chapter 14 quiz.


Assignment:  Chapter 14 Quiz review

Test 56 answers

1.  false
2.  false
3.  true
4.  true
5.  false
6.  false
7.  true
8.  true
9.  a.  no    b.  each point is mapped, but each one does not have a unique partner, since several of the points are mapped to the number 3 over and over.
10.  see graph
11.  yes
12.  -1, -1
13.  see graph

Test 57 answers

1.  12;  2
2.  (5, 12);  ( -8, 7)
3.  (-2, 5)
4.  R around A, -240 degrees
5.  9
6.  (4, 1)
7.  true
8.  true
9.  true
10.  true
11.  false
12.  true
13.  false
14.  segment AB
15.  segment BC
16.  Q
17.  C
18.  D
19.  D
20.  C
21.  Q
22.  see graph
23.  see graph

Geometry; 5/3

Our lesson today focused on how to determine the midpoints of segments and how the midpoint formula can be used to determine if segments bisect or not.  We went through several examples together and graphed a few figures before getting started on the assignment.


Assignment:  section 13-5;  page 545-546;  WE  #1-12, 14, 17, 18

Honors Geometry; 5/3

We continued our work with transformations today by going over how to work with dilations.  These can either be expansions or contractions, and all the shapes that result are similar to the original figure.  We went through the process of how to use vectors in working with this transformation and then went through a couple of coordinate examples before getting started on the assignment.


Assignment:  section 14-5;  page 596;  WE  #1-23

Geometry; 5/2

Welcome to May!  We continued to work with coordinate geometry today by taking a look at what vectors are and how to calculate them.  Using the x and y axes, we went over how vectors are connected to what we already know and how they can be used to determine both the magnitude and direction of a movement.  We went through several examples together before getting started on the assignment.


Assignment:  section 13-4;  page 541-542;  WE  #1-25 all

Honors Geometry; 5/2

Welcome to May!  We continued working on transformations today by showing the students how to work with rotations of figures.  We went over how to rotate clockwise, counterclockwise, and how to rotate around different points.  We learned 3 rules for rotations and then went over a few examples together before starting the assignment.


Assignment:  section 14-4;  page 590-591;  WE  #1-30, 34