Geometry; 3/31

We used the time today to introduce the basic skills of constructions.  We went over how to copy a segment and an angle.  We also went through how to add and subtract segments, as well as how to bisect an angle.

Assignment:  Basic constructions worksheet  #1-10

Honors Geometry; 3/31

The students got back their chapter 10 tests on constructions today and we went over any questions they may have had on their drawings.  We then went through a short introductory lesson on working with the area of rectangles to start off chapter 11.  We went over the basic formula of the area of a rectangle and how to use our previous knowledge of trig ratios to help figure out the base and heights of rectangles.


Assignment:  section 11-1;  page 426-427;  WE 1-31;  skip every 3rd problem

Geometry; 3/30

We took part II of an algebra skills inventory test today.  This will be used by both students and teachers for placement and curriculum adjustment in our algebra and geometry classes.  When they finished the test, the students got started on their assignment.


Assignment:  evaluating equations review;  page 419;  #1-18 all,  25-32 all

Honors Geometry; 3/30

We used today's class to work on an intro algebra review assignment for the upcoming chapter.  With several students still needing to take the test from yesterday due to the 9th grade field trip, part of the class took the test and the other part worked on the intro assignment.

Assignment:  page 419;  evaluating formulas review;  #1-32 all

Geometry; 3/29

We took part I of an algebra skills inventory test today.  This will be used by both students and teachers for placement and curriculum adjustment in our algebra and geometry classes.  When they finished the test, the students got started on their assignment.


Assignment:  graphing review;  page 113;  #1-22 all, 23-40 odd

Honors Geometry; 3/29

We turned in the chapter 10 reviews and entry tasks today at the beginning of the period.  The students then took the rest of the period taking the chapter 10 test.


Assignment:  none;  extra credit puzzle option

Geometry; 3/28

Today was the chapter 9 test.  The students turned in their chapter 9 review sheets and entry tasks before taking the test in class.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 3/28

We wrapped up our study of constructions today by going over the homework and taking a look at geometric means one more time before working on the review sheet.  The bulk of the period was spent completing the review sheet and getting any further questions answered about constructions.

Assignment:  Chapter 10 review sheet


Chapter 10 Test tomorrow

Geometry; 3/27

We worked through one more triangle proof today involving triangles to review the various concepts that we are working with in circles.  We also walked through 2 more combo problems together that involve multiple circle concepts from chapter 9.  The students then got started on their chapter 9 review sheets.

Assignment:  Chapter 9 Review sheet

Test on Chapter 9 Tomorrow

Circles

1.  90
2.  65
3.  30
4.  30
5.  95
6.  180
7.  105
8. 255
9. 4
10.  10
11.  35
12.  5 radical 3
13.  68
14.  60
15.  7.2
16.  x = 65;  y = 115
17.  95
18.  70
19.  9 radical 21
20.  14.5

Practice 36;  Angles and Segments

1.  100
2.  26
3.  70
4.  50
5.  155
6.  90
7.  40
8.  20
9.  90
10.  110
11.  6
12.  13.3
13.  40
14.  12
15.  x = 6 or x = 4


Practice 37;  Chapter 9 Practice

1.  AD
2.  OA, OD, OC
3.  AC or AD
4.  BA or BC
5.  110
6.  55
7.  90
8.  55
9.  70
10.  5
11.  120
12.  30
13.  15
14.  4
15.  8
16.  2


1.  5
2.  PR, PQ, PS
3.  tangent
4.  inscribed
5.  58
6.  arc RQ and arc QS;  arc RP and arc PS
7.  RP and PS
8.  AD = 9;  BC = 5
9.  arc JK = 130;  arc HKJ = 310
10.  LM = 3 radical 3

Honors Geometry; 3/27

We went through our final lessons on constructions today by taking a look at how proportional segments can be drawn using a compass.  We went through how to split segments into even numbered parts (using multiple bisecting steps) and odd numbered parts (using a reference line and parallel lines).  We also saw how to create a geometric mean between two different segments.



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

Geometry; 3/24

We continued our work with special cases of angles and segments in circles today by taking a look at larger combination problems that involve several of the concepts that we have been working on.  We went through a couple together before getting started on the homework assignment.


Assignment:  9-6 and 9-7 review worksheet

Honors Geometry; 3/24

We continued our work with constructions today by demonstrating how to construct circles and the various tangents that go along with them.  We used our previous knowledge of perpendicular lines to do this, and also revisited what it meant to either inscribe or circumscribe a figure involving a circle.  The students then got started on their assignment.


Assignment:  Section 10-4;  pg. 395;  WE  #1-10, 12-15

Geometry; 3/23

We continued our work with circles today by taking a look at how to calculate segment lengths in circles.  Each of these segments either intersect inside of or outside the circle.  We went through the two different rules for each type of segment and then a few problem examples together.  The students then got started on their homework.

Assignment:  section 9-7;  p. 363-365;  CE #1-6;  WE #1-9 (skip #8), 13-20

Honors Geometry; 3/23

We continued our work with concurrent lines today by taking a look at what perpendicular bisectors and altitudes do.  These constructions involved finding the circumcenter and orthocenter, respectively.  Each one of these points have unique characteristics that can be used in other applications.  We also took at look at how these points differ between acute, right, and obtuse triangles.


Assignment:  section 10-3;  page 388-389;  WE  #1-8, 11-14;  page 391;  #1-4

Geometry; 3/22

We introduced the concept of interior angles today, along with exterior angles.  Both have a formula that is based on similar triangles.  We worked to interpret several diagrams so that we can choose the correct formula to plug into.  After 4-5 examples, the students got started on their homework.


Assignment:  Section 9-6;  page 358;  CE #1-9;  page 359-360;  WE 11-21

Honors Geometry; 3/22

We continued our work with constructions today by taking a look at concurrent lines.  There are 4 examples of these types of constructions and we covered two of them today.  In triangles, the three angle bisectors meet to form the incenter of the triangle.  This point is the center of the inscribed circle in the triangle.  The three medians of a triangle meet to form the centroid of the triangle, which is the center of gravity.  This point has a mathematical relationship from the vertex to the median of 1/3 the total and 2/3 the total.  We did a couple of sample calculations using this before getting started on the assignment.


Assignment:  Constructions worksheet sections 10-1 to 10-4

Geometry; 3/21

We continued our work with inscribed angles today by taking a look at what I refer to as combination problems.  These are diagrams that have multiple variables that involve solving several steps to answer the question.  We went through a few examples of these before demonstrating a couple of triangle proofs using circles.  This is a skill that will be tested as a bonus question on the chapter 9 test, but going over them helps to review the concepts of the properties of angles and arcs in circles.


Assignment:  inscribed angles worksheet +  page 354-355;  WE #1-10, 12, 19, 21

Honors Geometry; 3/21

We continued our work with various constructions today.  We went over how to construct altitudes, medians, and perpendicular bisectors of triangles.  These skills were then used to begin constructing basic shapes that we have worked with during the year.  (rectangles, squares, rhombi, parallelograms)


Assignment:  section 10-2;  page 384;  WE  #14-24 all

Geometry; 3/20

We continued our work with circles today by taking a look at how inscribed angles are calculated.  We went over the basic concept that the inscribed angle is equal to 1/2 the intercepted arc.  We then went through 4 shortcuts on how to use this concept with a variety of drawings.  

Assignment:  inscribed angle worksheet + page 353;  CE #4-9

Honors Geometry; 3/20

We continued our work with constructions today by taking a look at how to construct both parallel and perpendicular lines in a variety of different scenarios.  We also took at look at how to construct specific number values of angles  (90, 45, 22.5, 60, 30, 15, 7.5) by using what we know about triangles.


Assignment:  section 10-2;  page 383;  WE  #1-12 all,  page 378,  WE 17-20

Geometry; 3/17

We turned in the chapter 9 quiz review to start the period.  The students then took the rest of the time to work on the chapter 9 quiz.

Assignment:  none;  extra credit puzzle option

Honors Geometry; 3/17

We continued our work with constructions today by going over how to copy triangles using 3 different methods -  ASA, SSS, and SAS.  All of these involve working with either copying angles or copying segments.  We also demonstrated how to add and subtract angles.

Assignment:  section 10-1;  page 378-379;  WE  #1-5, 7-15, 23, 24

Geometry; 3/16

Our lesson today focused on finishing up the notes from yesterday and showing a few different types of problems involving chords and distances from the center of a circle.  The students then spent the rest of the time working on their review sheet for the chapter 9 quiz tomorrow.


Assignment:  Chapter 9 Quiz review

Answer Key:

Basic Terms;  Tangents

1.  segment OT, segment OB
2.  segment BT
3.  line AB
4.  line TS
5.  segment AB, segment BT
6. point T
7.  8
8.  8n
9.  90
10.  segment QP congruent to segment QR
11.  perpendicular
12.  6
13.  6 radical 2
14.  ABCD
15.  15
16.  8
17.  28
18.  15
19.  18
20.  12

Arcs, Central Angles, and Chords

1.  90
2.  135
3.  135
4.  225
5.  45
6.  55
7.  20
8.  60 degrees
9.  150 degrees
10.  11 or 1 o'clock
11.  12
12.  8 radical 3
13.  60
14.  120
15.  120
16.  4 radical 3
17.  9
18.  9
19.  24
20.  14

Arcs and Chords

1.  x = 6;  y = 3.8
3.  8.9
5.  8.1
problem without a number:  8 radical 3
7.  11.4
9.  6.1
11.  9.4
13.  9.9

Honors Geometry; 3/16

We got back the chapter 9 test today on circles and the students had a chance to ask any question on it that they may have had.  We then got started on our construction unit on how to use a compass and a straight edge.  Today's introduction involved copying segments and angles, adding and subtracting segments, and bisecting angles.  These are all skills that need to be mastered as we move forward.


Assignment:  Constructions intro worksheet

Geometry; 3/15

We continued our work with circles today by taking a look at how arcs and chords are related.  We went through several examples in the notes as we used congruent triangles to help us develop the concepts.  We then got started on the homework during the last half of the period.


Assignment:  section 9-4;  page 347;  WE #1-13;  page 341;  CE #1-13

Honors Geometry; 3/15

We turned in our entry task sheets and chapter 9 review sheets to start off the period.  We then spent the remainder of the period taking the chapter 9 test.


Assignment:  none;  extra credit puzzle option

Geometry; 3/14

We continued our work with circles today by taking a look at how central angles and arcs in circles are calculated.  We went over the definitions of minor arcs, major arcs, and semicircles.  We then demonstrated a few calculations before spending the rest of the period working on our assignment and eating pie to celebrate pi day.


Assignment:  Central angles and arcs worksheet

Honors Geometry; 3/14

We spent time going over the chapter 9 review sheet today and answering any questions that may have come up.  We then went through one more triangle proof that involved properties of circles.  The rest of the period was spent celebrating pi day by eating the pies that the students brought in.  We also worked on the 2nd review sheet for the test while we were eating pie!


Assignment:  Chapter 9 Review Sheet #2


Review Sheet Answers

Practice 36

1.  100
2.  26
3.  30
4.  50
5.  155
6.  90
7.  40
8.  20
9.  90
10.  110
11.  6
12.  13 1/3
13.  40
14.  12
15.  x = 6 or x = 4

Practice 37

1.  segment AD
2.  segment OA, segment OD, segment OC
3.  segment AC,  segment AD
4.  segment BA,  segment BC
5.  110
6.  55
7.  90
8.  55
9.  70
10.  5
11.  120
12.  30
13.  15
14.  4
15.  8
16.  2
17.  proof
               Statements                                       Reasons
          angle G congruent to angle H               given
        OF perp. to FG;  OI perp. to HI              given
       angle GFO and angle HIO rt. angles       def. of perp.
       angle GFO congruent to angle HIO        all right angles congruent
       OH congruent to OG                               all radii of same circle congruent
       triangle GFO congruent to tri. HIO         AAS
       OF congruent to OI                                 CPCTC
      EG congruent to HJ                                 in same circle, if chords are same
                                                                      distance from center, then chords
                                                                      are congruent

Geometry; 3/13

We continued working with tangents today by going over how to use triangle shortcuts with tangents in various types of drawings.  We also went over how to distinguish between and internal and an external tangent line.  Circles that are internally or externally tangent were also identified.


Assignment:  section 9-2;  page 335;  CE 1-3;  page 335-336;  WE #1-6, 8, 9 , 10, 16

Honors Geometry; 3/13

We went over several homework problems today involving our lesson from Friday.  We then went through 2 triangle proofs that involved properties of circles.  This is a topic that is review, but I also wanted the students to see how the new properties of circles can be used to prove triangles are either congruent or similar.  The students then got started working on their chapter 9 review packet.

Assignment:  Chapter 9 Review Packet

Geometry; 3/10

We continued our work with circles today by taking a look at some of the properties of tangents to circles.  The main concept used was that tangents to circles are also perpendicular to the radius of the circle at the point of tangency.  We can use this fact to work a variety of right triangle problems and determine values of tangent segments.  We went through a few examples together before getting started on the homework.


Assignment:  Tangents and Circles worksheet

Honors Geometry; 3/10

We continued our work with circles today by going over how to determine the lengths of chords associated with circles.  Just like angles, there were two separate guiding concepts:  one for interior segments and one for exterior segments.  We went over 3-4 examples of each and showed how each concept is derived from similar triangles.  The students then got started on their homework assignment.


Assignment:  section 9-7;  page 364-365;  WE #1-9;  13-20;  22, 23

Geometry; 3/9

We started a new unit today -- the study of circles!  We will continue to use triangles quite a bit to study this new topic, but today's lesson focused on how to make some new drawings with different vocabulary words.  We introduced the terms secant, tangent, point of tangency, chord, diameter, radius, and circumference.  There were a couple of short calculation problems that we demonstrated as well.

Assignment:  section 9-1;  page 330;  CE #1-11;  page 330-331;  WE 1, 2, 5-15

Honors Geometry; 3/9

We continued our work today with circles by taking a look at different types of angles that are associated with a circle.  We went over interior angles formed by two chords/secants, and then exterior angles formed by two chords or secants.  Each type of angle is based on similar triangles and a proportion.  We went over two new formulas to use while working these types of problems before getting started on the assignment.

Assignment:  section 9-6;  page 358-359;  CE #1-9;  page 359-360;  WE #1-21

Geometry; 3/8

We turned in our review sheet and entry tasks for chapter 8 to start off the period.  The students then took the rest of the period to take the chapter 8 test.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 3/8

We continued our work with circles today by going over how to work with inscribed angles and inscribed quadrilaterals.  We went over several examples showing various shortcuts that can be taken in determining the inscribed angles and the intercepted arcs.  We saw how diameters, common arcs, and tangent angles all can be used to quickly calculate these problems.


Assignment:  section 9-5;  page 353;  CE #4-9;  page 354;  WE #1-10, 12, 19, 21

Geometry; 3/7

We spent some more time today going over how to work trig application problems.  We then reviewed 3-4 concepts together in preparation for the test tomorrow.  The bulk of the period was spent working on the chapter 8 review sheet.

Assignment:  chapter 8 review sheet

Right Triangles

1.  3 radical 10

2.  2 radical 3 over 3

3.  13

4.  25

5.  12 radical 2

6.  2 radical 11

7.  obtuse

8.  acute

9.  right

10.  x = 8 radical 3;  y = 4 radical 21;  z = 8 radical 7

11.  x = 7;  y = 7 radical 3

12.  x = 12

13.  x = 28

14.  x = 34

15.  34 degrees

Applications of Trigonometry

1.  26 m

2.  21 m

3.  51 m

4.  48 degrees

5.  135 m

6.  2400 m

7.  140 m

Practice 33;  Trigonometry

1.  radical 3 over 2

2.  1/2

3.  radical 3 over 1

4.  1/2

5.  radical 3 over 2

6.  radical 3 over 3

7.  .9397

8.  .8480

9.  .2493

10.  77 degrees

11.  8 degrees

12.  61 degrees

13.  x = 27

14.  x = 17

15.  x = 51

16.  x = 11

17.  x = 26

18.  52 degrees

19.  a.  sketch    b.  150 m

page 301;  CE  #1-9  special right triangle practice

1.  6 radical 2

2.  10

3.  6 radical 2

4.  10

5.  6.5

6.  3 radical 3

7.  4 radical 2

8.  10 radical 3

9.  9 radical 2

Honors Geometry; 3/7

We answered a few questions to start with today in terms of going over the review sheet.  After about 5 minutes of review, the students then took the rest of the period to take their chapter 9 quiz.


Assignment:  none;  extra credit option

Geometry; 3/6

We continued our work with trigonometry today by taking a look at how to set up and solve applications of trigonometry problems.  The main concept of today's lesson was how to draw the right triangle that will be used to solve the problem.  We discussed how to work with angles of elevation, angles of depression, and % grade problems.  We went through 3 examples together before getting started on the homework assignment.


Assignment:  Trig. Applications WS + page 319;  WE  #3, 5, 10a, 11

Honors Geometry; 3/6

We went over several homework problems together in getting ready for the chapter 9 quiz tomorrow.  We then reviewed 4 of the main concepts that we have covered so far in working with circles.  The rest of the time was spent working on the ch. 9 quiz review sheet.


Assignment:  Chapter 9 Quiz Review sheet


Answers:

Basic Terms;  Tangents

1.  segment OT, segment OB
2.  segment BT
3.  line AB
4.  line TS
5.  segment AB,  segment BT
6.  point T
7.  8
8.  8n
9.  90
10.  segment QP and segment QR
11.  perpendicular
12.  6
13.  6 radical 2
14.  ABCD
15.  OP = 15
16.  RS = 8
17.  HI = 28
18.  15
19.  18
20.  12

Arcs, Central Angles, and Chords

1.  90
2.  135
3.  135
4.  225
5.  45
6.  55
7.  20
8.  60
9.  150
10.  11 or 1 o clock
11.  12
12.  8 radical 3
13.  60
14.  120
15.  120
16.  4 radical 3
17.  9
18.  9
19.  24
20.  14

Tangents, Arcs, and Chords

1.  5
2.  segments PR, PQ, and PS
3.  tangent
4.  inscribed
5.  58
6.  arc RQ and arc QS  or arc RP and arc PS
7.  segment RP and segment PS
8.  AD = 9;  BC = 5
9.  arc JK = 130;  arc HKJ = 310
10.  LM = 3 radical 3

Geometry; 3/3

We continued our work with trig ratios today by solving a few different varieties of right triangles.  We went over 3-4 examples together in class before getting started on the assignment towards the end of the period.


Assignment:  Solving Right Triangles worksheet

Honors Geometry; 3/3

We continued our work with circles today by going over how to work with problems involving arcs and chord lengths.  We demonstrated the importance of drawing a diagram and using the right triangle relationships that we have already worked on.  We went over 4-5 examples together using two main concepts of working with the diameter and perpendicular lines.


Assignment:  section 9-4;  page 347-348;  WE  #1-13, 17-19, 21,22


Chapter 9 Quiz on Tuesday, March 7

Geometry; 3/2

We continued our work with trigonometry ratios today by taking a look at the sine and cosine ratios and how they work.  We went over how to find both angles and sides with these ratios and introduced the SOH CAH TOA memory device to help figure out which ratio to use.  We then got started on our homework assignment.


Assignment:  Trig. Ratio worksheet + page 315;  WE  #13-16

Honors Geometry; 3/2

We continued our work with circles today by going over how to identify arc types and central angles.  We discussed major arcs, minor arcs, and semicircles and how to label each one.  We also went over how to find the measurements of these arcs by using the central angles.  Our final topic was an illustration of how to use central angles to determine location on the globe and how geometry is used in calculating longitude and latitude.


Assignment:  section 9-3;  page 341;  CE  #1-13 all;  page 341-342;  WE  #1-11, 16-20 all

Geometry; 3/1

We started our study of trigonometry today by going over what the tangent ratio is and how to use it.  We used the ratio to determine both sides and angles of right triangles.  We also went over how to use a trig ratio table and/or our scientific calculators to help solve these problems.


Assignment:   section 8-5;  page 306;  CE  #1-7;  page 308-309;  WE  #1-18, 21

Honors Geometry; 3/1

We continued our study of circles today by taking a look at the different properties involved with tangent lines and tangent circles.  We went over several drawing examples and a couple of calculation examples to demonstrate the different concepts that the assignment will involve.


Assignment:  section 9-2;  page 335;  CE #1-3;  page 335-337;  WE  #1-6, 8-10, 16, 17