Geometry; 3/30

We worked through some more practice examples involving inscribed angles today.  The students then spent the rest of the period working on their assignment involving more examples of inscribed angles.


Assignment:  inscribed angles WS #2 + pg. 354-355;  WE 1-9, 19-21

Honors Geometry; 3/30

The students took part 2 of the chapter 9 test today.


Assignment:  none

Have a great Spring Break!

Geometry; 3/29

We continued on in our study of circles today by taking a look at inscribed angles and the arcs they intercept.  We went through several examples and shortcuts involving inscribed angles to demonstrate how to calculate the values of these angle types and their arcs in circles.  The students then got started on their homework assignment.


Assignment:  Inscribed / Central angle worksheet +  page 353;  CE 4-9

Honors Geometry; 3/29

We spent some time at the beginning of the period to review some questions from chapter 9.  After going over these together, the students then took part 1 of the chapter 9 test. We will take part 2 of the test tomorrow in class.


Assignment:  none;  extra credit puzzle option

Geometry; 3/28

We went over a few questions together on the reviews to start the period.  The students then spent the rest of the time taking the chapter 9 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 3/28

We spent some time going over homework and reviewing a few larger drawings that ask multiple types of questions.  The students then got started on their reviews for the chapter 9 test.  Part 1 of the test will be given tomorrow and then part 2 will be Friday.


Assignment:  Chapter 9 Test Review


Test 36   Angles and Segments

1.  90
2.  290
3.  55
4.  180
5.  140
6.  320
7.  a.  105, 75;    b.  opposite angles are supplemental
8.  140
9.  20
10.  angle IHJ
11.  a.  132;   b.  66
12.  a. 75;   b.  8
13.  52
14.  132
15.  49
16.  12
17.  4.8
18.  12
19.  10
20.  6 or 12
21.  9
22.  2

Test 37    Chapter 9 Test

1.  chord
2.  center;  on the circle
3.  90
4.  70
5.  150
6.  one
7.  a.  140     b.  110
8.  0 ,  180
9.  80
10.  100
11.  100
12.  280
13.  50
14.  40
15.  congruent chords have congruent arcs in the same circle
16.  congruent arcs in the same circle have congruent central angles
17.  7 radical 2
18.  21
19.  50
20.  10
21.  60
22.  75
23.  68
24.  don't do proof
25.  12
26.  16
27.  9 radical 10
28.  6

Geometry; 3/27

We spent some time today reviewing various drawings and figures in getting ready for the quiz tomorrow.  We went over 4-5 problems together before the students got started on their quiz review sheet.


Assignment:  Chapter 9 Quiz Review


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


Arcs and Chords

2.  x =3;  y = 1.1
4.  x = 4.6
6.  x = 5.2
un numbered question;  x = 70
8.  x = 9.4
10.  x = 6.3
12.  x = 7.1
14.  x = 8.4

Honors Geometry; 3/27

We continued our work with circles today by taking a look at interior and exterior segments.  Just like yesterday with other angles, these types of segments are determined by working with similar triangles.  We went through both of the equations and did 2-3 sample problems with each one.  The students then got started on their assignment.


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

Geometry; 3/26

We continued our work with circles today by taking a look at how to work with chords and segments.  The drawings that we learned all involved some sort of right triangle being formed from an intersection of chords and diameters/radii.  The shortcuts involved with these drawings all involved the pythagorean theorem and congruent triangles.  We went through 4-5 examples together before getting started on the assignment.


Assignment:  Section 9-4;  page 347-348;  WE 1-13, 17, 18

Honors Geometry; 3/26

We continued our study of circles today by taking a look at how to calculate other angles involved in circles.  These angles occur both inside and outside of circles and are formed from the intersections of two lines/segments.  The interior angles are found using the equation :  interior angle = 1/2 (arc 1 + arc 2).  The exterior angles are found by using the equation:  exterior angle = 1/2 (large arc - small arc).  We went through 3-4 examples of 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; 3/23

Today's topic centered on what a central angle was and how to determine its value while working with the entire circle.  We also talked about how to calculate arc measurements in this process.  The foundation of the topic was that the central angle is always equal to the arc it intercepts on the circle.


Assignment:  Section 9-3;  page 341;  CE 1-13;   page 341-342;  WE  1-8, 10-11

Honors Geometry; 3/23

Our work today focused on how to determine the value of inscribed angles.  The first part of the lesson focused on how to recognize inscribed angles and their intercepted arcs in various types of drawings.  We then went through several different shortcuts with drawings in order to calculate the values of inscribed angles and/or intercepted arcs. 


Assignment:  section 9-5;  page 353;  CE 4-9;  page 354-355;  WE 1-10, 12, 19, 21

Geometry; 3/22

Today was day #2 of our work with tangents.  We went over a calculation drawing that involved isosceles triangles to begin the lesson and indicated the shortcuts that students can take to solve these types of problems.  We also demonstrated the difference between internal and external tangent lines and internal and external tangent circles.


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

Honors Geometry; 3/22

We spent a short amount of time at the beginning of the period answering some questions on the review assignment before the students turned them in.  The rest of the time was spent taking the chapter 9 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 3/21

We went over the homework problems today before reminding everyone about the different types of drawings involved in the quiz tomorrow.  We reviewed how to draw circles and spheres, and which drawings to recognize for the shortcuts they afford.  The students then got started on their review assignment.


Assignment:  Chapter 9 Quiz review


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; 3/21

We continued our work with circles today by taking a look at the different properties that tangent lines have in circles.  We went through single tangent lines and how the pythagorean theorem is used extensively to solve these types of problems.  We also took a look at a few drawings that involve two tangents to the same circle that originate from the same point.

Assignment:  Tangents to Circles worksheet + algebra review problems  (factoring)

Honors Geometry; 3/20

We continued our study of circles today by taking a look at the relationships between arcs and chords. We went through several different drawings that showed how right triangles are a big part of studying circles.  We demonstrated several methods of solving problems before getting started on the assignment.


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

Geometry; 3/20

We started our study of circles today by taking a look at the various terms involved with circles.  Vocab terms like radius, diameter, chord, tangent, and secant were a few of the several topics we covered today.  The lesson focused mainly on how to draw the different figures associated with circles and spheres.


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

Geometry; 3/19

The students turned in their chapter 8 entry task and review assignment at the beginning of the period.  The rest of the period was spent taking the chapter 8 test.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 3/19

Our study of circles today focused on minor arcs, major arcs, semicircles and central angles.  We demonstrated how these terms are related and what each one of them refers to when looking at a circle diagram.  We went through some central angle and arc calculations together as well before the students got started on their assignment.


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

Geometry; 3/16

We spent some time reviewing some major topics from chapter 8 today:  geometric means, similar triangles, pythagorean theorem, specials right triangles, and trig application problems.  The students did one of each type as a group and then got feedback on their success.  They then got started on the chapter 8 review sheet.  The chapter 8 test is on Monday.


Assignment:  Chapter 8 review sheet


Review Sheet Answers

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 meters
2.  21 meters
3.  51 meters
4.  48 degrees
5.  135 meters
6.  2400 meters
7.  140 meters

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.  0.9397
8.  0.8480
9.  0.2493
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 meters

Honors Geometry; 3/16

We continued our study of circles today by taking a look at the different types of tangent lines that are associated with circle drawings.  We also went over how to use the property of tangent lines being perpendicular to the radii of circles in a variety of problem types.  The students then got started on their assignment.


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

Geometry; 3/15

We continued our work with trig application problems today by showing how to handle %grade problems and scenarios involving shadows.  Both of these types of problems were demonstrated and practiced together before the students got started on their assignment.


Assignment:  Trig application WS +  page 319;  WE 10,11 ;  page 315;  WE 14-16

Honors Geometry; 3/15

The students got their tests back today and were able to go over any questions that they still had.  We then got started on the study of our unit on circles.  Today was largely an introduction to several of the vocabulary words associated with circles.   The students were able to get familiar with these new terms through a variety of drawings before getting started on the assignment.


Assignment:  section 9-1;  page 330  CE 1-11;  page 330-331;  WE 2, 6-15, 18

Geometry; 3/14

Our topic today centered on how to work with trig application problems.  We discussed how to use angles of depression and angles of elevation in today's lesson and how to draw diagrams involving them.  We went over 2-3 examples together before the students got started on their assignment.


Assignment:  section 8-7;  page 318-319;  WE 1-6, 9

Honors Geometry; 3/14

The students turned in their ch. 8 reviews and entry tasks at the start of the period.  They then took the rest of the period to complete the chapter 8 test.


Assignment:  none;  extra credit puzzle option

Geometry; 3/13

We continued our work with trig ratios today by getting some more practice with a variety of right triangle drawings.  We went how to work with isosceles triangles and how to solve right triangles.  The students' goal was to become more proficient with how to work with their calculators and to determine the correct trig ratio to use.


Assignment:  Solving Right Triangles worksheet +  page 314-315;  WE 5-12

Honors Geometry; 3/13

We spent some more time today going over the chapter 8 review and demonstrating a few more trig application problems.  The students then got started on their assignment.


Assignment:  Ch. 8 Review #2


Special Right Triangles page

1.  acute
2.  obtuse
3.  acute
4.  right
5.  not possible
6.  right
7.  right
8.  obtuse
9.  right
10.   x = 11;  y = 11 radical 2
11.  x = radical 2;  y = 2
12.  x = 5;  y = 5
13.  x = 40;  y = 20 radical 3
14.  x = 3 radical 3;  y = 6 radical 3
15.  x = 4 radical 2
16.  x = 7 radical 3;  y = 60
17.  x = 2 radical 3 over 3;   y = 2 radical 3;  z = 4;  v = 4 radical 3 over 3
18.  8 radical 3
19.  24 radical 2
20.  30

Sine, Cosine, and Tangent Ratios page

1.  12/13
2.  5/13
3.  12/13
4.  12/5
5.  5/12
6.  5/13
7.  .0523
8.  .8660
9.  1.1106
10.  .9816
11.  19 degrees
12.  61 degrees
13.  68 degrees
14.  50 degrees
15.  36 degrees
16.  39
17.  12
18.  19
19.  48
20.  34
21.  x = 44;  y = 57
22.  x = 17;  y = 11

Trigonometry Application Problems

1.  24.1 km
2.  26.0 meters
3.  about 74 degrees
4.  a.  8.5 degrees   (about 9 degrees)      b.  about 4.7 feet
5.  angle A = 35.4 degrees;  angle C = 54.6 degrees;  side AB = 15.5

6.  angle Z = 31 degrees;  side XY = 12.6;  side YZ = 24.5

Geometry; 3/12

We continued our study of trigonometry today by taking a look at the sine and cosine ratios.  We went through examples of each ratio to demonstrate how both sides and angles can be determined using the ratios.  We also went through how to use the correct keys on the scientific calculators to speed up the problem solving method.

Assignment:  Sine/Cosine/Tangent worksheet

Honors Geometry; 3/12

After answering the homework questions, we went over how to solve right triangles today and how to work with diagrams with overlapping right triangles.  Each method involved a couple of demonstration problems before the students practiced some problems on their own.

Assignment:  Chapter 8 Review Sheet #1

Geometry; 3/8

The topic today involved the beginning of our study of trigonometry.  We went over how to use the tangent ratio today.  We went through 4-5 examples of how this ratio is used to determine both side lengths and angles in right triangles.


Assignment:  section 8-5;  page 306;  CE 1-7;  page 308;  WE 1-16

Honors Geometry; 3/8

We continued our work with trigonometry today by taking a look at how to set up application problems.  Each one of these problems involves drawing a diagram to fit the word description.  Vocab words such as angle of depression, angle of elevation, and % grade were discussed and demonstrated as to how the diagrams should be drawn.  The students then got started on their assignment.


Assignment:  section 8-7;  page 318-319;  WE 1-6, 9-11;  page 309;  WE 19-21

Geometry; 3/7

We took a few minutes at the start of the period to go over some of the review questions together.  After this was done, the students turned in their ch. 8 quiz reviews and spent the rest of the period taking the chapter 8 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 3/7

We continued our work with trig ratios today by taking a look at the sine and cosine ratios.  We went over 4-5 problems together of how to use these ratios before getting started on the assignment.  An emphasis was made on helping students learn how to use the trig function keys on their scientific calculators.

Assignment:  section 8-6;  page 314-216;  WE #1-21 all

Geometry; 3/6

We spent time today reviewing the concepts involved in the first part of our study of right triangles.  We went over a couple of problems together before spending the bulk of the period working in pairs on several types of review problems.  The students spent the last 10-15 minutes of the period getting started on their chapter 8 quiz review.  The quiz is tomorrow.

Assignment:  Chapter 8 quiz review.


Similarity in Right Triangles

1.  10
2.  10 radical 2
3.  2 radical 30
4.  2 radical 5 over 5
5.  radical 3 over 3
6.  1/3
7.  12
8.  6
9.  8 radical 3
10.  x = 4;  y = 2 radical 5;  z = 4 radical 5
11.  x = 5 radical 2;  y = 5 radical 6;  z = 5 radical 3
12.  x = 15
13.  x = 12
14.  x = 8 radical 5
15.  x = 20
16.  x = 5 radical 2
17.  x = 10
18.  2.5 meters
19.  3 radical 2 cm
20.  40

Converse of Pythagorean Theorem

1.  acute
2.  obtuse
3.  acute
4.  right
5.  not possible
6.  right
7.  right
8.  obtuse
9.  right
10.  x = 11;  y = 11 radical 2
11.  x = radical 2;  y = 2
12.  x = 5;  y = 5
13.  x = 40;  y = 20 radical 3
14.  x = 3 radical 3;  y = 6 radical 3
15.  x = 4 radical 2
16.  x = 7 radical 3;  y = 60
17.  x = 2 radical 3 over 3;  y = 2 radical 3;  z = 4;  v = 4 radical 3 over 3
18.  8 radical 3
19.  24 radical 2
20.  30

Honors Geometry; 3/6

The students got back their ch. 8 quizzes today and had a chance to ask any questions that they were not able to figure out.  We then got started on the next topic in our unit on right triangles.  We went over the first part of trigonometry today by showing how to work with the tangent ratio.  I demonstrated how to use the trig tables in the book and also how to make use of the trig function keys on the scientific calculators.  After 4-5 examples, the students got started on their assignment.


Assignment:  section 8-5;  page 308-309;  WE 1-18 all

Geometry; 3/5

We continued our work with special right triangles today by taking a look at combination drawings with 2 types of triangles.  We went over 4-5 examples together of these types of drawings before the students got started on their assignment.


Assignment:  Special Right Triangles worksheet

Honors Geometry; 3/5

The students turned in their chapter 8 quiz reviews at the beginning of the period.  They then used the rest of the period to take the chapter 8 quiz.

Assignment:  none;  extra credit puzzle option

Geometry; 3/2

Our topic today centered on how to work with special right triangles.  These triangles have unique angle pairs that repeat themselves in many types of problems.  We went over how to work with the 45-45-90 triangles and the 30-60-90 triangles.  We worked through several different examples before getting started on the assignment.


Assignment:  Section 8-4;  page 301;  CE 1-9;   page 302;  WE 1-16

Honors Geometry; 3/2

We spent the first part of the period going over the homework and answering a number of questions on how to work with special right triangles.  We then reviewed similarity in right triangles and how to set up geometric mean proportions.  The students then got started on their reviews.  The chapter 8 quiz is on Monday, March 5.

Assignment:  Chapter 8 Quiz review WS


Chapter 8 Quiz on Monday, March 5

Test 31

1.  1/6
2.  3 radical 3
3.  4 radical 3
4.  5 radical 3 / 3
5.  radical 7
6.  RQS ;  SQT
7.  a.  ST    b.  RT
8.  8 radical 5
9.  4 radical 5
10.  (8 radical 5) squared +  radical 5) squared = 20 squared
        or 320 + 80 = 400
11.  8
12.  SQ  or  8
13.  In a right triangle, the square of the hypotenuse is equal to the sum of the square of the legs
14.  7
15.  2 radical 3
16.  6 radical 2
17.  5
18.  12 m

Test 32

1.  a.  right      b.  If the square of 1 side of a triangle is = to the sum of the squares of the other 2 sides, then the triangle is a right triangle
2.  obtuse
3.  right
4.  not possible
5.  acute
6.  17 < n < 23
7.  a.  5    b.  5 radical 2
8.  a.  5 radical 2       b.  5 radical 2
9.  a.  6      b.  3 radical 2
10.  j = 7;  k  = 7 radical 3
11.  k = 3 radical 6;  t = 6 radical 2
12.  j = radical 3;  t = 2 radical 3
13.  1 : radical 3 : 2
14.  5 radical 2 / 2
15.  10


Special Right Triangle Practice Sheet

1.  a = 4;  b = 2 radical 2
2.  x = y = 2 radical 2
3.  x = 3;  y = 3 radical 2 over 2
4.  x = 6;  y = 3 radical 2
5.  x = y = 3 radical 2
6.  x = y = 2 radical 3
7.  x = 8 radical 3;  y = 8
8.  u = 4;  v = 2 radical 3
9.  u = 16;  v = 8 radical 3
10.  x = 4 radical 15;  y = 4 radical 5
11.  x = 10;  y = 5
12.  x = 5 radical 3;  y = 5
13.  u = v = 8
14.  x = 8 radical 3;  y = 4 radical 3
15.  a = 3 radical 3 over 2;  b = 3/2
16.  a = 22;  b = 11
17.  a = radical 6;  b = radical 2
18.  m = 7 radical 2 over 2;  n = 7 radical 2 over 2

Geometry; 3/1

We worked on the converse of the pythagorean theorem today, using the 3 numbers to determine if a triangle is right, acute, or obtuse.  We also took a look at some of the history of the pythagorean theorem together through a video clip.


Assignment:  section 8-3;  page 296-297;  CE 1-6, 9, 10;  WE 1-14

Honors Geometry; 3/1

We continued our work with special right triangles today by going over drawings that deal with combinations of triangles.  We worked to solve one triangle at a time until we get to the unknown variable.  We went through 4-5 examples together before getting started on the assignment.


Assignment:  special right triangles worksheet +  page 302;  WE 21-26