Geometry; 2/28

We continued our work with the Pythagorean Theorem today by taking a look at how this equation is used to solve a variety of problems involving other figures.  The key thing is to find a right triangle within other figures.  We went through 4-5 examples together using a variety of figures before the students got started on their assignment.

Assignment:  Section 8-2;  page 292-293;  WE 13-30

Honors Geometry; 2/28

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 1-20

Geometry; 2/27

Our topic today involved working with the pythagorean theorem with a variety of triangles and number values.  This foundational skill will be utilized throughout the next three chapters, so we went over several versions of these problems together to make sure there was good understanding.  The students then got started on their assignment.

Assignment:  section 8-2;  page 291,  CE 5-18;  page 292;  WE 1-12

Honors Geometry; 2/27

We continued our work with right triangles today by showing how to use the converse of the pythagorean theorem.  We went over how to determine if triangles are right, acute, or obtuse using this converse.  We also watched a short video clip of the history of the pythagorean theorem.


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

Geometry; 2/26

We continued working on similarity in right triangles today by going through several more examples of how to find the geometric means in a variety of drawings.  We continued to use our notecards and worked on being able to chose the correct proportion for each problem.

Assignment:  Similar Triangles worksheet

Honors Geometry; 2/26

Our study of right triangles focused on the Pythagorean Theorem today by taking a look at how to solve various types of problems using this famous equation.  We went over the basic problems first, and then moved on to working with various other shapes that involve the pythagorean theorem as well.  We worked through 3-4 examples together before getting started on the assignment.


Assignment:  section 8-2;  page 292-293;  WE 1-30 all

Geometry; 2/23

The students spent a little time studying their perfect squares to begin the period.  They then took a perfect squares and simplifying radicals quiz in class.

Assignment:  none

Honors Geometry; 2/23

The students spent a little time studying their perfect squares to begin the period.  They then took a perfect squares and simplifying radicals quiz in class.

Assignment:  none

Geometry; 2/22

We introduced the concept of similarity in right triangles today by taking a look at how one large right triangle can actually contain 3 similar triangles.  We derived some proportions together that illustrated what a geometric mean is and then went over how to calculate different parts of these similar triangles.


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

Honors Geometry; 2/22

We continued to work on similar right triangles and geometric means today.  I went over 3 more examples of different ways to accomplish these types of problems before getting started on the homework.  We also took a practice perfect squares quiz. 


Assignment:  similar triangles worksheet +  page 289;  WE 32, 34-36, 38

Geometry; 2/21

We continued our work with radicals today by reviewing the concept of how to multiply and divide radical expressions.  Along with this topic, we also learned how to rationalize the denominator in case the denominator holds an irrational value.  We went over 4-5 examples together before getting started on the homework.


Assignment:  Operations with Radicals worksheet

Honors Geometry; 2/21

We introduced the concept of similarity in right triangles today by taking a look at how one large right triangle can actually contain 3 similar triangles.  We derived some proportions together that illustrated what a geometric mean is and then went over how to calculate different parts of these similar triangles.


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

Geometry; 2/20

We introduced our study of right triangles today by reviewing the algebra skill of working with radicals and square roots.  Knowing the perfect squares and being able to factor them out of a variety of numbers is something that the students will need to be able to do repeatedly during this chapter.  We went over 4-5 examples of how to simplify radicals today before getting started on a review worksheet.


Assignment:  Simplifying Radicals worksheet

Honors Geometry; 2/20

We continued our work with radicals today by going over how to multiply and divide radical expressions.  Included in this was factoring polynomials under the radical.  The skill of rationalizing the denominator was also shown and practiced.


Assignment:  Radicals worksheet #2

Honors Geometry; 2/16

We introduced our study of right triangles today by reviewing the algebra skill of working with radicals and square roots.  Knowing the perfect squares and being able to factor them out of a variety of numbers is something that the students will need to be able to do repeatedly during this chapter.  We went over 4-5 examples of how to simplify radicals today before getting started on a review worksheet.


Assignment:  Radical Review WS #1;   #1-16, 33-62

Geometry; 2/15

We spent time today reviewing for the chapter 7 test tomorrow.  We went through several problems together with partners before getting started on the review sheet.

Assignment:  Chapter 7 Review worksheet



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; 2/15

The students took the chapter 7 test today in class.


Assignment:  none

Geometry; 2/14

The lesson today focused on using proportional lengths in different types of scenarios from what we encountered yesterday.  We went over 3-4 examples of how to use total values in the ratios to make the various problem types shorter.  The students also practiced one more similarity proof on their own before getting started on the assignment.


Assignment:  Proportional lengths worksheet

Honors Geometry; 2/14

We spent some time today going over a couple more types of similar triangle proofs in preparation for tomorrow's test.  We also went over any homework questions the students had before getting started on the review assignment.


Assignment:  Chapter 7 test review


Chapter 7 Test

1.  5c2 / 7a2
2.  1/25
3.  2/9
4.  72
5.  2hs
6.  t + h / h
7.  g/s
8. g/s or h/t
9.  10
10.  10
11.  4/3
12.  triangle DAC
13.  AA for similar triangles
14.  3:5
15.  AC ; AD; CD
16.  15
17.  statements                               reasons
     given statements                       given
 angle K and angle S rt. angles      def. of perpendicular
angle K congruent to angle S        all right angles congruent
angle A congruent to angle A       reflexive
triangle AKT similar to tri. ASE    AA for similar triangles
AK/AB = AT/ AE                           if sim. triangles, corr. sides are proportional
AK/AT = AS / AE                           prop. of proportions

Test 27

1.  need CD = 10 or DE = 2
2.  AE parallel BD;  angle A congruent to angle B;  angle E congruent to angle D
3.  BC,  AE
4.  yes, by SSS for similar triangles
5.  proportional lengths and parallel lines
6.  a. yes
     b.  yes
     c.  no
     d.  yes
7.  x = 4
8.  x = 12
9.  x = 6.4
10.  x = 12.5
11.  x = 7.5
12.  x = 60

Test 26

1.  yes
2.  yes
3.  no
4.  yes
5.  no
6.  SAS for sim. triangles
7.  AA for sim. triangles
8.  none
9.  none
10.  AA for sim. triangles
11.  SSS for sim. triangles
12.  1.  angle 1 and angle 2 are complementary
            angle 2 and angle 3 are complementary

       2.  complements of the same angle are congruent
       3.  reflexive
       4.  AA for sim. triangles
       5.  corr. sides of sim. triangles are proportional
       6.  cross multiplication

Similarity Proofs

1,                       statements                            reasons
     IE parallel to VO                                     given
    angle D cong. to angle D                          reflexive
    angle I cong. to angle V                          if lines II, then corr. angles congruent
   tri. DIE similar to tri. DVO                      AA for similar triangles
   ID/IV = ED/EO                                        corr. sides of sim. triangles proportional


2.                 statements                                reasons
       AE parallel BD                                     given
      angle C cong. to angle C                       reflexive
      angle B cong. to angle A                       if lines parallel, corr. angles congruent
     tri. CBD sim. to tri. CAE                       AA for sim. triangles


3.             statements                                  reasons
       AB parallel to DC                                given
       angle 1 congruent to angle 2               vertical angles congruent
      angle ABE cong. to angle CDE           if lines parallel, AIA congruent
      tri. AEB similar to tri. CED                 AA for similar triangles

Geometry; 2/13

Our topic today focused on working with other figures that have proportions built into them.  We worked with segments, parallel lines, triangles and angle bisectors with the purpose of being able to quickly put proportions together in order to solve problems.  We went through several pattern examples together in going through the shapes and then the students got started on their homework.

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

Honors Geometry; 2/13

Our topic today focused on working with other figures that have proportions built into them.  We worked with segments, parallel lines, triangles and angle bisectors with the purpose of being able to quickly put proportions together in order to solve problems.  We went through several pattern examples together in going through the shapes and then the students got started on their homework.


Assignment:  section 7-6;  page 272-273;  WE 1-25   (skip 13, 14, 17-19)

Geometry; 2/12

We continued our work with similarity postulates today by going over 3 more proof examples together.  Each drawing was a little different from those that we have already seen.  The students then got started on their assignment working both with proofs and with similarity calculations.


Assignment:  Similarity Proofs WS + Similar Polygons WS

Honors Geometry; 2/12

We continued our work with similarity proofs today by demonstrating how to work with both SAS and SSS similarity postulates.  We went over how to identify similarity drawings and choose the correct postulate.  The students then got started on their homework.






section 7-5;  page 264-265;  CE 1-6;  page 266-267;  WE 1-16

Geometry; 2/9

We continued our work with similarity proofs today by demonstrating how to work with both SAS and SSS similarity postulates.  We went over how to identify similarity drawings and choose the correct postulate.  The students then got started on their homework.

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

Honors Geometry; 2/9

We continued our study of similar triangles today by taking a look at the Angle-Angle Postulate for similar triangles.  The AA postulate is one that is used in similarity proofs, so we went through 2-3 similarity proofs together to demonstrate how these work.  The students then got started on their assignment.

Assignment:  section 7-4;  page 256;  CE 1-8;  page 257-259;  WE 1-19, 21, 24, 27

Geometry; 2/8

We continued our study of similar triangles today by taking a look at the Angle-Angle Postulate for similar triangles.  The AA postulate is one that is used in similarity proofs, so we went through 2-3 similarity proofs together to demonstrate how these work.  The students then got started on their assignment.

Assignment:  section 7-4;  page 256;  CE 1-8;  page 257-258;  WE 1-7, 10-13, 15, 17, 21, 23

Honors Geometry; 2/8

The students turned in their chapter 7 quiz reviews at the beginning of the period.  The rest of the period was spent taking the chapter 7 quiz.

Assignment:  none;  extra credit puzzle option

Geometry; 2/7

After turning in the chapter 7 quiz review, the students spent the period taking the chapter 7 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 2/7

The students took the AMC test today, so our class time was just a devoted work day.  The chapter 7 quiz will take place tomorrow.


Assignment:  finish Chapter 7 Quiz review


Answer Key:

Ratio and Proportion

1.  3:4
2.  5:4
3.  2:3
4.  5:2
5.  1:5
6.  5:2
7.  8/5
8.  2/15
9.  2:5:10
10.  10:7:17
11.  3/4
12.  5/4
13.  16
14.  3/4
15.  10/4  or 5/2
16.  5/10 or 1/2 or x + 2 / 8
17.  x = 15/7
18.  x = 48
19.  x = 16
20.  27
21.  13.3
22.  27
23.  16
24.  18
25.  18
26.  15

Similar Polygons

1.  sometimes
2.  always
3.  always
4.  sometimes
5.  sometimes
6.  never
7.  5:9
8.  82
9.  54
10.  36k/5
11.  5:9
12.  x = 29;  y = 30
13.  x = 21;  y = 15
14.  x = 15;  y = 12
15.  x = 10.67;  y = 15

Similarity Diagram Problems

4. a. 2:1
b.  2
c.  150
d.  10
e.  1:2

5. a.  x = 11;  y = 9
b.  x = 10.7;  y = 120
c.  x = 39.4;  y = 23.1
d.  x = 7.5;  y = 166

Proportion Problems

14.  a = 23
16.  x = 13
18.  n = 3/2
20.  x = 14
22.  b = 3

24.  x = 32/11

Geometry; 2/6

We spent time today working on several different types of review problems for the chapter 7 quiz tomorrow.  Students worked with partners on 4 different problem types before getting started on their review assignment towards the end of the period.


Assignment:  Chapter 7 Review

Answer Key:

Ratio and Proportion

1.  3:4
2.  5:4
3.  2:3
4.  5:2
5.  1:5
6.  5:2
7.  8/5
8.  2/15
9.  2:5:10
10.  10:7:17
11.  3/4
12.  5/4
13.  16
14.  3/4
15.  10/4  or 5/2
16.  5/10 or 1/2 or x + 2 / 8
17.  x = 15/7
18.  x = 48
19.  x = 16
20.  27
21.  13.3
22.  27
23.  16
24.  18
25.  18
26.  15

Similar Polygons

1.  sometimes
2.  always
3.  always
4.  sometimes
5.  sometimes
6.  never
7.  5:9
8.  82
9.  54
10.  36k/5
11.  5:9
12.  x = 29;  y = 30
13.  x = 21;  y = 15
14.  x = 15;  y = 12
15.  x = 10.67;  y = 15

Similarity Diagram Problems

4. a. 2:1
b.  2
c.  150
d.  10
e.  1:2

5. a.  x = 11;  y = 9
b.  x = 10.7;  y = 120
c.  x = 39.4;  y = 23.1
d.  x = 7.5;  y = 166

Proportion Problems

14.  a = 23
16.  x = 13
18.  n = 3/2
20.  x = 14
22.  b = 3

24.  x = 32/11

Honors Geometry; 2/6

We spent time today working through several review problems in preparation for the chapter 7 quiz.  After finishing the work with their seat partners, the students then got started on the chapter 7 quiz review.

Assignment:  Chapter 7 quiz review


AMC test is tomorrow in the commons;  Chapter 7 Quiz is on Thursday.

Geometry; 2/5

We continued working on similarity problems today by taking a look at how to do problems in which the figures overlap.  We went through 3-4 examples of this type of problem before the students got started on their assignment.


Assignment:  Overlapping Similarity worksheet + page 251;  #24, 27

Honors Geometry; 2/5

We continued our work with similarity today by taking a look at how to set up similarity problems using different figures.  We went through 3-4 problems together of finding the scale factor between figures and then determining various unknown values.  The students then got started on their assignment.

Assignment:  section 7-3;  page 250-251;  CE 1-10 all;  WE 15-27 all

Geometry; 2/2

The topic today focused on how to use proportions to work with similar polygons.  Similarity is based on congruent angles and proportional sides, so we went through 3-4 sample problems showing how to determine a scale factor and then use it to determine unknown quantities.  The students then got started on their assignment.


Assignment:  Similar Polygons worksheet +  Self Test 1;  page 252, #1-15

Honors Geometry; 2/2

Our work today focused on how to use ratios and proportions together to solve geometric problems.  We went over a quick reviewing of techniques used to solve proportions (cross multiply and divide).  We also demonstrated 5 properties of proportions that are useful in working different types of similarity problems.  The students then got started on their assignment.


Assignment:  section 7-2;  page 247-248;  WE #1-28, 33-35

Geometry; 2/1

Our topic today was focused on how to use ratios and proportions together.  This algebra skill is necessary for working similarity problems, so we spent some time going through the various techniques to solve proportions and then how to use the properties of proportions in multiple ways.  We went through 4-5 examples together before getting started on the assignment.


Assignment:  Section 7-2;  page 247-248;  WE 1-25 all, 27, 33-35

Honors Geometry; 2/1

The students got back their chapter 13 test today and were able to ask any questions that they may have had.  We then got started with our next unit of study:  similarity.  This topic is closely tied to how ratios are used to solve problems, so we went through 4 different uses for ratios in a variety of types of geometry problems.  The students then got started on their homework.


Assignment:  section 7-1;  page 243;  CE 1-4;  page 243-244;  WE 1-32 all