Geometry; 2/28

We reviewed a few questions together from the chapter 8 review sheet at the beginning of class.  The students then spent the remainder of the period working on the chapter 8 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 2/28

The students got back their chapter 8 test today and were given the opportunity to ask questions on any items they may have missed.  We then got started on our next unit of study -- circles.  We went over some basic drawings and terminology today.  Some of the terms are familiar to the students, while others are new.  These terms are necessary to work with the problems that are coming our way during this unit of study.

Assignment:  section 9-1;  page 330;  CE #1-11;  page 330-331;  WE 2, 5-15, 18

Geometry; 2/27

We spent some time reviewing combination problems involving special right triangles today as a review for our ch. 8 quiz tomorrow.  We also reviewed how to work with classifying triangles and similarity problems involving right triangles.  We worked 4-5 examples together before getting started on the review sheet.

Chapter 8 Quiz tomorrow.

Assignment:  Ch. 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.  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

The Pythagorean Theorem and its Converse

1.  5 in
2.  5 miles
3.  8.6 km
4.  14.1 miles
5.  2 radical 14
6.  8 radical 3
7.  2 radical 26
8.  radical 10
9.  right triangle;  225 = 225
10.  right triangle;  256 = 256
11.  acute triangle;  121 < 196
12.  acute triangle;  2352.3 < 2577.3
13.  yes
14.  yes
15.  obtuse
16.  acute
17.  obtuse
18.  right

Honors Geometry; 2/27

We collected our chapter 8 review materials at the beginning of the period.  The students then took the rest of the period to complete the chapter 8 test.


Assignment:  none;  extra credit puzzle option

Geometry; 2/24

We went through an entry task that focused on special right triangles before going over last night's homework.  We then took our second perfect squares quiz of this chapter.

Assignment:  Special Right Triangles worksheet  (#1-18 all)

Honors Geometry; 2/24

We spent time going over part of our chapter 8 review sheet today during the shortened periods.  At the end of the period, the 2nd review was handed out and the students got started working on it.

Test on chapter 8 on Monday, Feb. 27

Assignment:  Ch. 8 Review #2


Answers to 2nd page of Review Sheet #1

We went over the first page of the review sheet in class on Friday.

22.  x = 4 radical 2;  y = 4 radical 6;  z = 8 radical 2
23.  a.  r/t        b.  r/s        c.  s/t             d.  r/t
24.  cos 41 = y/15;    sin 49 = y/15
25.  tan 26 = 20/y;    tan 64 = y/20
26.  sin 40 = 8/y;     cos 50 = 8/y
27.  tan angle 1 = 8/5
28.  cos angle 1 = 6/10
29.  sin angle 1 = 7/25
30.  15 meters

Solving Right Triangles page

9.  AB = 17.9;  angle A = 63.4 degrees;  angle B = 26.6 degrees
13.  angle Z = 62.5 degrees;  XZ = 17.8;  XY = 15.8
15.  angle D = 59 degrees;  DE = 10.5;  DF = 20.4
18.  229.4 meters
19.  height going up:  21.8 ft;  height going down = 42.0 ft;  total height = 63.8 ft



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; 2/23

We continued our work with right triangles today by going over how to work with two different types of special right triangles.  The 45-45-90 triangle and the 30-60-90 triangles are both special cases that have a repeatable pattern.  We went over how to work with the shortcuts of this pattern in a variety of problems before getting started on the assignment.


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

Honors Geometry; 2/23

We went over our final topic in chapter 8 today by studying how to solve right triangles.  This involves finding all the sides and angles of a given right triangle.  Trig ratios, triangle angle sum theorem, and the pythagorean theorem are all used to go through this process.  We also reviewed a few more examples of how to set up trig ratio application problems and the drawings that go with them.  The students then got started working on their review sheets.

Assignment:  Chapter 8 review sheet

Chapter 8 Test on Monday, Feb. 27

Answers to 2nd page of Review Sheet #1

We went over the first page of the review sheet in class on Friday.

22.  x = 4 radical 2;  y = 4 radical 6;  z = 8 radical 2
23.  a.  r/t        b.  r/s        c.  s/t             d.  r/t
24.  cos 41 = y/15;    sin 49 = y/15
25.  tan 26 = 20/y;    tan 64 = y/20
26.  sin 40 = 8/y;     cos 50 = 8/y
27.  tan angle 1 = 8/5
28.  cos angle 1 = 6/10
29.  sin angle 1 = 7/25
30.  15 meters

Solving Right Triangles page

9.  AB = 17.9;  angle A = 63.4 degrees;  angle B = 26.6 degrees
13.  angle Z = 62.5 degrees;  XZ = 17.8;  XY = 15.8
15.  angle D = 59 degrees;  DE = 10.5;  DF = 20.4
18.  229.4 meters
19.  height going up:  21.8 ft;  height going down = 42.0 ft;  total height = 63.8 ft



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; 2/22

We continued our work with the pythagorean theorem today by going over how to use the converse of the theorem to verify if the figure is a right triangle.  We also used the theorem to classify triangles as either obtuse or acute based on the results of using the pythagorean theorem.  We watched a short video clip about the history of the theorem as well to give students a background of how the idea came about and what it was used for.

Assignment:  section 8-3;  page 297;  WE  #1-14 all;  page 304;  Self Test 1;  #1-7

Honors Geometry; 2/22

We continued to work on using the trig ratios today by going over how to work with trig application problems.  These types of problems involve all 3 trig ratios, but also involve knowing how to draw the correct diagram.  We covered how to draw angles of depression, angles of elevation, and problems dealing with a % grade.  We went through 3 examples together before getting started on the assignment.


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

Geometry; 2/21

We continued our work with the Pythagorean theorem today by going over how it is used to solve questions with a variety of different shapes.  We reviewed the rhombus, square/rectangle, isosceles triangle, and trapezoid properties in today's lesson and showed how they can all be incorporated into a right triangle and the pythagorean theorem.


Assignment:  section 8-2;  page 292-293;  WE  #7-27

Honors Geometry; 2/21

We continued our work with trigonometry today by going over how to use the sine and cosine ratios.  These two additional ratios are used very much like the tangent ratio, only with different side combinations.  We went through 3-4 examples using both of these ratios before getting started on the homework assignment.


Assignment:  section 8-6;  page 314-316;  WE  #1-21 all

Geometry; 2/17

We went over our homework today and answered any more questions on similar right triangles that the students had.  We then introduced the topic of the Pythagorean Theorem to the students and laid the simple foundation that many of them have seen before.  Using this theorem will be integral to much of what we do next week, so we just did a quick review of the basics together.  The students then took a short quiz on simplifying radicals before getting started on the assignment.


Assignment:  Pythagorean Theorem worksheet  (#1-15)

Honors Geometry; 2/17

We introduced the topic of trigonometry today by going over the tangent ratio and how to use it.  We went through the methods of finding both angles and sides together before getting started on the assignment using this first trig ratio.


Assignment:  section 8-5;  WE  #1-18

Geometry; 2/16

We continued our work with similar triangles today by going a more complex version of what we were introduced to on Tuesday.  The 3 similar triangles have a variety of different relationships, and the students used their notecards to find those relationships and solve the problems in more complex drawings today.  We also continued to practice with working on radicals in preparation for the radicals quiz tomorrow.


Assignment:  Similar Triangles WS +  page 289,  WE #31-34

Honors Geometry; 2/16

We went over a few questions from the review sheet today before taking the chapter 8 quiz in class.

Assignment:  none;  extra credit puzzle option

Geometry; 2/15

school closed due to icy conditions

Honors Geometry; 2/15

school closed due to icy conditions

Geometry; 2/14

We started our work on the geometry portion of chapter 8 today after finishing up our review of radicals over the past couple of days.  We went over what a geometric mean refers to in our lesson.  We developed a series of drawings that we put on a notecard that the students can use as a reference tool throughout the chapter.  this includes on tests and quizzes.  We went through how to identify a geometric mean on various types of drawings and then how to solve for various segment lengths.

Assignment:  section 8-1;  page 288;  WE  #11-26

Honors Geometry; 2/14

We took a perfect squares quiz today in class before going over a few more review problems in preparation for the quiz tomorrow.  The students then used the rest of the period to work on their review sheet.  The answers to the review sheet appear below.


Assignment:  Section 8.1 to 8.4 review sheet

Chapter 8 Quiz tomorrow

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; 2/13

We continued our work with reviewing radicals today by going over how to multiply and divide using radicals.  This algebra skill is one that will be used over and over in the next few chapters, so we want to have a good handle on it before moving forward.  We also went over how to rationalize the denominator once radicals have been divided.  At the end of the period we had our first practice quiz on the perfect squares that we are learning.  We will have a few of these practices before taking the real quiz at the end of the week.


Assignment:  Operations with Radicals worksheet

Honors Geometry; 2/13

We continued our work with right triangles today by going over how to work with special right triangles.  The 45-45-90 triangle and the 30-60-90 triangle are right triangles that are used heavily in right triangle problems, and there are some shortcuts to working with them that we went over today.  The sooner the students memorize these shortcuts, the easier the problems will become.  We went over several together as we started practicing the process of learning these patterns.


Assignment:  section 8-4;  page 302-303;  WE  #1-26, 29

Geometry; 2/10

The students got back their chapter 7 test today and had a chance to ask any questions that they might have had.  We then got started on the next topic as we move into right triangles.  The skill that we worked on today was dealing with how to simplify radicals.  This is purely an algebra skill and one that will be used over and over again in the next couple of chapters.  We will continue working with radicals on Monday as we review how to both multiply and divide radicals.

Assignment:  simplifying radicals worksheet

Honors Geometry; 2/10

We continued with our work on the Pythagorean Theorem today by showing how to make use of it's converse.  We confirmed right triangles today using the the side lengths of triangles, but we also were able to classify triangles as either acute or obtuse depending on the values that the pythagorean theorem provided us with.  We went over a few examples together before getting started on the assignment.  The students then also took their mental math perfect squares quiz at the end of the period.


Assignment:  section 8-3;  page 297;  WE  #1-14 all;  pg. 304;  Self Test 1;  #1-7 all

Geometry; 2/9

Snow day;  school cancelled

Honors Geometry; 2/9

Snow day;  school cancelled

Geometry; 2/8

We answered a couple of questions that came up on the review sheet at the beginning of the period.  We then turned in our chapter 7 entry task sheets and chapter 7 review sheet before taking the chapter 7 test.


Assignment:  extra credit puzzle option

Honors Geometry; 2/8

We continued our work with right triangles today by going over how to solve problems using the Pythagorean Theorem.  This is an equation that is very familiar to many students, so the foundation of this lesson has already been laid by previous math courses.  We then showed how to use this equation to work with a variety of figures that we have already studied.  We went over how a triangle, a rhombus, a square, and a trapezoid can all be worked on using the pythagorean theorem.  The students then got started on their assignment.


Assignment:  section 8-2;  page 292-293;  WE  #1-29, 33

Geometry; 2/7

We went over the homework from yesterday that dealt with proportional lengths in various figures.  We then did a couple final review problems in getting ready for the test tomorrow.  The main focus was to do one more proof and then also to be able to handle what I call a "shadow" problem.  These types of problem involve making your own sketch based on an explanation from a sentence or two describing a shadow scenario of two objects.

The rest of the time was spent working on the review packet.


Assignment:  Chapter 7 Review Sheet


Postulate for Similar Triangles

1.  RAS
2.  AC
3.  ARC
4.  AR
5.  yes, AA
6.  not similar
7.  yes, AA
8.  yes, AA
9.  not similar
10.  yes, AA
11.  x = 10.4;  y = 9
12.  x = 6.4;  y = 2.5
13.  x = 16;  y = 20

Theorems for Similar Triangles

1. SSS;  ABC similar to EFD
2.  SAS;  ACS similar to ART
3.  SAS;  ABC similar to DEC
4.  SAS;  PQR similar to SQT
5.  SSS;  JKL similar to PMN
6.  AA;  ROS similar to MTS
7.  yes
8.  a.  SNU;  b.  1:3
9.  no

Proportional Lengths

1.  yes
2.  no
3.  yes
4.  no
5.  no
6.  yes
7.  yes
8.  no
9.  6
10.  5
11.  42
12.  20
13.  14
14.  2
15.  10
16.  8

Similar Polygons

1.  x / 4y
2.  a / 5
3.  1/4
4.  8
5.  5/4
6.  4
7.  7.5
8.  x = 16;  y = 15
9.  x = 25;  y = 13.5
10.  ABC similar to EFD;  AA
11.  ABE similar to CBD;  SAS
12.  ABC similar to DFE;  SSS
13.  x = 4.2
14.  x = 14.4
15.  x = 4

Honors Geometry; 2/7

We went through another similar triangle example on our entry task.  We then spent some time practicing our perfect squares in preparation for the quiz at the end of the week.

Several students were out taking a national math exam, so we spent the rest of the time working on our mental logic skills playing checkers.

Assignment:  none

Geometry; 2/6

We finished up our last topic in chapter 7 today.  After reviewing another type of similar triangle proof, we went over how to work with proportional lengths with various figures.  We demonstrated how segments, parallel lines, and triangles can all be divided up proportionally to solve for various parts.  These often involve shortcuts from what we have previously worked on, so hopefully the problems will go more quickly for the students.  The students then got started on their assignment.


Assignment:  section 7-6;  page 272-273;  WE  #1-12 all, 15, 16, 20, 21;    page 274;  Self-Test 2;  #1-11 all

Honors Geometry; 2/6

We continued our work with similar right triangles today by taking another look at how to use the geometric means in right triangles to solve various types of problems.  We went over a couple more examples using the notecard we created on Friday and then the students got to work on their assignment.  We also went through a practice perfect squares quiz to get the students used to what they will be asked to do later on this week.

Assignment:  similar triangle WS (#1-18) +  page 289;  WE  31-33

Honors Geometry; 2/3

We started our chapter 8 lessons today by going over how to work with right triangles and similarity.  There was a particular drawing that we went over together to see that one large right triangle actually involves a total of 3 similar right triangles.  We went through a few problems like this in order to demonstrate how to solve problems with these triangles, and how to find the geometric mean.  This was a new concept (geometric mean) that we used our algebra skills in order to handle.


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

Geometry; 2/2

We continued our work with similar triangles today by going over two more methods of working with similar triangles.  The SSS theorem and the SAS theorem were the two topics that we covered in class today.  Each one involved some short calculations to determine if sides were proportional before confirming the 2 triangles were similar.  We then went over a couple more similar triangle proofs together before getting started on the assignment.


Assignment:  Section 7-5;  page 264-265;  CE #1-6;  page 266-267;  WE  #1-12, 15

Honors Geometry; 2/2

We continued our work with radicals today by going over how to multiply and divide radicals.  We also reviewed the process of rationalizing the denominator.  These algebra skills will be very useful as we move forward into chapter 8 and right triangles starting tomorrow.


Assignment:  Radicals review WS #3

Geometry; 2/1

We went over a short entry task to review a couple of topics for the quiz today to start the period.  We then turned in our ch. 7 quiz review sheets and spent the rest of the period taking the chapter 7 quiz.


Assignment:  extra credit puzzle option

Honors Geometry; 2/1

After going through a brief entry task, we spent the rest of the period taking the chapter 7 test.

Assignment:  extra credit puzzle option