Geometry; 2/29

Happy Leap Day!

We continued our study of circles today by taking a look at central angles, major arcs, and minor arcs today.  We went over several vocabulary words as well as some initial calculations involving central angles.  After these examples, the students got started on their homework.


Assignment:  section 9-3;  page 341;  CE  1-13;   page 342-343;  #1-8. 10, 11

Honors Geometry; 2/29

Happy Leap Day!

We continued our work with polygons today by taking a look at how to find the area of regular polygons.  We were introduced to the terms apothem and radius of various types of polygons.  We then went over a few examples before getting started on the assignment.


Assignment:  section 11-4;  page 443-444;  WE  #1-21 all

Geometry; 2/25

We continued our work with circles today by taking a look at the properties of tangents in circles.  We went over how to use the pythagorean theorem in working with circles to prove a line is tangent, and also how congruent triangles can be used to find some shortcuts in circles problems.  After a few examples, the students then got started on their assignment.


Assignment:  tangent to circles worksheet + page 335;  WE  1-6, 8

Honors Geometry; 2/25

We continued our work on areas of polygons today by taking a look at trapezoids.  We reviewed what we had studied previously in regards to the median of trapezoids and then used triangles to figure out a formula for the area.  After a few sample problems, the students got started on their assignment.


Assignment:  section 11-3;  page 436-437;  WE  1-9 odds, 10-23 all,  29, 30

Geometry; 2/24

We started our new unit today that deals with circles.  Much of the lesson centered on learning new vocabulary words that will be included in our study.  The new terms involved chords, secants, tangents, and arcs.  We went over a few quick calculation problems with circles as well before starting the assignment.


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

Honors Geometry; 2/24

We continued our work with areas today by taking a look at the area of parallelograms, triangles, and rhombuses.  The three formulas were given, but the main part of the lesson involved how to figure our the parts that are then plugged into the formulas.  These parts involve shortcuts from the unit on right triangles.  The students then got started on the assignment at the end of the class period.


Assignment:  section 11-2;   page 431-433;  WE  1-24;  35, 36

Geometry; 2/23

We turned in our chapter 8 review sheet at the beginning of the period.  The students then took the period to do the chapter 8 test.

Assignment:  extra credit option

Honors Geometry; 2/23

We went over our Chapter 9 test in class today.  Remember the retake opportunity if you want to take advantage of it.  You can take a retake through the end of next week.  We also started the next chapter on the area of polygons.  We will skip chapter 10 and come back to it at the end of the year, so we are working with areas of rectangles in chapter 11.

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

Geometry; 2/22

We went over the homework before working through several review problems together for the chapter 8 test tomorrow.  The students then got to work on their review worksheet in preparation for the test.

Assignment:  Chapter 8 Review Sheet

Honors Geometry; 2/22

We turned in our chapter 9 review packet today at the beginning of the period.  The students then took the chapter 9 test in class today.


Assignment:  extra credit puzzle option

Geometry; 2/19

We went over the homework before finishing off the chapter today with a few more application problem types and working with how to solve right triangles.  We did a couple of examples of each before the students got started on their assignment.


Assignment:  solving right triangles worksheet +  page 319;  WE  5, 6, 10a, 11

Honors Geometry; 2/19

We answered homework questions together before reviewing a few more circle proofs.  The students then got started working on their chapter 9 review sheet.  The test is on Monday.

The answers to the review sheet will be posted on this site later in the weekend.


Assignment:  Chapter 9 review sheet


Test 36 answers;  Angles and Segments

1.  90
2.  290
3.  55
4.  180
5.  140
6.  320
7.  a.  105, 75     b.  opposite angles in inscribed quadrilaterals are supplemental
8.  140
9.  20
10.  a.  angle IHJ     b.  if 2 inscribed angles intercept the same arc, then the angles are congruent
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.  22

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.  in the same circle, congruent chords have congruent arcs
16.  in the same circle, congruent minor arcs have congruent central angles
17.  7 radical 2
18.  21
19.  50
20.  10
21.  60
22.  75
23.  68
24.  skip the proof
25.  12
26.  16
27.  9 radical 10
28.  6

Geometry; 2/18

We continued our work with trig functions today by taking a look at application problems involving the trig ratios.  Essentially these are word problems that use the different trig functions to solve them, but they all involve drawing a picture first.  We went through 3-4 of these problem types together before getting started on the assignment.



Assignment:  Trig. Application worksheet (31-36) + page 314-315;  WE 1-12

Honors Geometry; 2/18

We finished up our study of circles today by going over how to calculate the lengths of different segments inside and outside of circles.  We went over 3 different equations together today that can be used to do these types of problems and then worked 3 sample problems to show the students how to make use of the equations.  The rest of the time was spent working on the assignment.


Assignment:  section 9-7;  page 364-366;  WE #1-9; 13-20; 22, 23

Geometry; 2/17

We continued working with trig functions today by going over how to use the sine and cosine functions.  We went through several examples to be able to use our calculators better in a variety of problem types.  The students then got started on their assignment.


Assignment:  Trig Ratio worksheet +  page 315;  WE  14-16

Honors Geometry; 2/17

We continued our work with circles today by going over how to work with other types of angles.  The categories were interior and exterior angles and we went through several different examples of how to calculate these types of angles and the arcs they involve.  The students then got started on their assignment at the end of the period.


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

Geometry; 2/16

After the long weekend, we got back to studying right triangles today by taking a look at the first trigonometric ratio -- the tangent.  We went over the definition of tangent and how to use it to solve questions concerning right triangles.  We also spent time learning how to use the trig functions in our calculators.  After several examples, the students got started on their assignment.


Assignment:  section 8-5;  page 306;  CE 1-7;  page 308-309;  WE  #1-19 all

Honors Geometry; 2/16

After the long weekend, we got back to studying circles today and the angles that are found inside them.  The lesson today focused on inscribed angles and the different ways that they can be calculated in circles.  We went through several examples together before getting started on the assignment.


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

Geometry; 2/12

We turned in the chapter 8 quiz review today at the beginning of the period before taking the chapter 8 quiz in class.  The students had the period to work on it.

Assignment:  extra credit option

Honors Geometry; 2/12

After turning in our review for chapter 9, the students took the chapter 9 quiz in class today.


Assignment:  extra credit option

Geometry; 2/11

We continued working with special right triangles today by going over how to work with triangle combinations.  We went through 3-4 examples together before getting started on our review assignment in preparation for the quiz tomorrow.  Tomorrow's quiz is over sections 8-1 to 8-4.

Assignment:  Chapter 8 quiz review sheet


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.  8 radical 5
15.  20
16.  5 radical 2
17.  10
18.  2.5
19.  3 radical 2
20.  40

Special Right Triangles

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; 2/11

We turned in our chapter 9 review sheet and then took the chapter 9 quiz in class today.


Assignment:  none;  extra credit option

Geometry; 2/10

We continued reviewing similar triangles and the geometric mean by going over a couple of questions with a warm up problem.  After homework corrections were made, we then spent time on the next lesson that involved special right triangles.  The 45-45-90 triangle and the 30-60-90 triangle are two right triangles that are used extensively, so we went over the short cut ratios that each one has in order work through problems more quickly.  We went through several examples together before getting started with the homework assignment.


Assignment:  section 8-4;  page 301;  CE  #1-9 all;  page 302;  WE #1-20 all

Honors Geometry; 2/10

We spent time going over homework to start the period before going through some review exercises for our quiz tomorrow.  We went through a circle proof, as well as several different types of drawings involving tangent lines together.  The students then got started on their review packet in preparation for the quiz tomorrow.   The answers to the packet will appear on this blog later in the day.


Assignment:  Review worksheet section 9-1 to 9-4


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
11.  Proof steps below

             angle AOD congruent to angle COD                           Given
            angle AOD + angle AOB = 180                                    Angle Addition Postulate
            angle COD + angle BOC = 180                                    Angle addition postulate
            angle AOD congruent to angle BOC                            Substitution
            arc AB congruent to arc BC                                          in same circle, if central angle is
                                                                                                   congruent, then arcs are congruent

Geometry; 2/9

Our lesson today focused on checking and classifying triangles using the pythagorean theorem.  We reviewed obtuse and acute triangles before showing how calculations can determine these types of triangles as well.  After a few examples, the students got started on their assignment.

Assignment:  Converse of Pythagorean Theorem worksheet



Quiz over sections 8-1 to 8-4 is on Friday, Feb. 12

Honors Geometry; 2/9

We continued our work with circles today by going through the relationship between arcs and chords in the same circles.  We took a look at radii that are perpendicular to chords and saw the shortcuts from congruent triangles that we could use to solve problems.  After going through several problems together, we then got started on the assignment.


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

Geometry; 2/8

We went over our quiz from Friday to start the period today before getting into the lesson.  Today's lesson involved a couple of video clips on the history of the pythagorean theorem and then more types of problems that use the pythagorean theorem with different figures.  The goal in each problem was to find the right triangle and get the correct sides plugged into the equation.    We went over a few examples together before getting started on the assignment.


Assignment:  section 8-2;  page 292-293;  WE  #13-28 all

Honors Geometry; 2/8

We continued our work with circles today by taking a look at central angles and arcs.  New notation and vocabulary words were introduced, as was the use of the number 360 in order to work with circle calculations.  We went over several examples together before getting started on the assignment.


Assignment:  Section 9-3;  page 341;  CE  #1-13 odds;   page 341-342;  WE  #1-11 all, 14-20 all

Geometry; 2/5

We quickly introduced the use of the pythagorean theorem today, as we will work more with its use next week.  The rest of the time today was taken up with a perfect squares quiz and a short quiz on simplifying radicals.


Assignment:  section 8-2;  page 292;  WE 1-12

Honors Geometry; 2/5

We continued our work with circles today by taking a look at the properties that tangent lines have in connection to circles.  We talked about internal tangents and external tangents, as well as how to do some of the basic calculations with tangents using right triangles.


Assignment:  section 9-2;  page 335;  CE 1-3;   page 335-336;  WE  1-6, 8-10, 16, 17

Geometry; 2/4

We continued our work with similar triangles today by looking at several more types of problems involving the three geometric means we introduced yesterday.  The formulas were the same but the numbers involved included both radicals and whole numbers.  We did a few examples before the students got started on their assignment.


Assignment:  similarity in right triangles worksheet  1-25 odd

Honors Geometry; 2/4

We went over our chapter 8 test today to start the period before beginning the next chapter.  Chapter 9 deals with the topic of circles and today's lesson involved an introduction to a variety of vocabulary words that are part of circles.  We went over a few short calculations as well dealing with figures that are drawn inside the circles.  The students then got started on their assignment.


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

Geometry; 2/3

We began our work in chapter 8 today by taking a look at similarity in right triangles.  We went over what a geometric mean is and how it is calculated.  We also went through how to find the geometric means when there are three right triangles that are given to us.  After a few examples, the students then got started on their homework.

Assignment:  section 8-1;  page 288;  WE  #1-26 all

Honors Geometry; 2/3

After turning in the chapter 8 review, the students took the chapter 8 test in class.

Assignment:  extra credit option

Geometry; 2/2

We went over our chapter 7 test today to start class, as well as our homework assignment from last night.  We continued our work with perfect squares today with another practice quiz in a different format.  The quiz on perfect squares and working with radicals will take place on Friday.  Today's topic continued to focus on what to do with radicals.  Today we worked with multiplying and dividing radical expressions.  We also went over how to rationalize the denominator in a fraction.  We went through several examples together before the students got started on their homework.


Assignment:  Operations with Radicals worksheet

Honors Geometry; 2/2

We went over our first review sheet today for the chapter 8 test.  This was a longer assignment and the students had several questions to get answered.  We then spent a little time reviewing special right triangles together before getting started on the second review sheet.  The answers to this 2nd review sheet will be posted on this site later this afternoon.  Both review sheets will be turned in tomorrow before we take the chapter 8 test.


Assignment:  Chapter 8 review sheet #2

Answers to review sheet #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; 2/1

We got started working on chapter 8 today which deals with right triangles.  In order to have the necessary skills to work with the pythagorean theorem, we reviewed how to simplify radicals with both numbers and variables today.  This is an algebra skill, but it will be used heavily in this chapter, so we will spend a couple of days reviewing it before we begin our study of right triangles.


Assignment:  Simplifying Radicals worksheet;  1-38   do multiples of 3;  39-48 all

Honors Geometry; 2/1

We started our review of chapter 8 today by going over special right triangles again and also how to work with the geometric mean when there are three right triangles involved.  We did a few sample problems together before the students got started on the first of their chapter 8 review sheets.


Assignment:  Chapter 8 Review Sheet #1

Geometry; 1/29

After turning in our review sheet, the students took the chapter 7 test in class today.


Assignment:  extra credit puzzle option

Honors Geometry; 1/29

We went over the homework today and reviewed several trig application problems together.  The students then got started on their review worksheet #1 for the chapter 8 test.


Assignment:  Chapter 8 Review #1