Geometry; 12/20

We went over our homework assignment and answered any questions that the students had today before taking the final quiz of 2016!  The homework check quiz took the rest of the time in class.


Assignment:  none;

Merry Christmas and have a great break from school!

Honors Geometry; 12/20

We introduced the concept of what similar polygons are today by going through our final lesson of 2016!  We went through how to identify the congruent angles and the proportional sides in similar shapes and then worked through two different calculation problems together.  Finding the scale factor in every similarity problem is the key step to getting the correct answer.


Assignment:  section 7-3;  page 250-251;  CE  1-10 all;  WE  1-13 odd, 15-27 all


Merry Christmas and have a great break from school!

Geometry; 12/19

We continued our work with inequalities today by taking a look at how to work with inequalities in a single triangle.  We went through examples showing how to determine the longest/shortest sides of triangles and how they relate to the size of angles in the triangle.  We also went through the process of how to determine the range of values for the side lengths of a triangle.

Assignment:  section 6-4;  pg. 222-223;  WE 7-15;  Triangle Inequalities WS  (skip 31, 33)

Honors Geometry; 12/19

We continued our work with similarity today by going over how to work with proportions.  Solving proportions is an algebra skill that we will work with extensively in this chapter.  We went over 4 properties of proportions that will be helpful in this unit, as well as how to set up proportions based on diagrams of figures.  The students then got started on their homework assignment.


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

Geometry; 12/16

We had a short day today with the 2-hour delay and our winter assembly.  We spent the time explaining a little more about the scavenger hunt project together and also collecting last night's homework. The assignment today was some additional practice on some review topics.


Assignment:  section 6-2;  page 210;  CE 5-12

Honors Geometry; 12/16

The students got back their Chapter 6 Test from Wednesday and had a chance to look over their scores.  We then went through a brief lesson on working with fractions and setting up ratios from various figures.  These ratios will be used extensively in this chapter as we work on the concept of similarity.

Assignment:  Section 7-1;  page 243-244;  WE  #1-30 all

Geometry; 12/15

School was cancelled due to snow!  Have a fun and safe day!

Honors Geometry; 12/15

School was cancelled due to snow!  Have a fun and safe day!

Geometry; 12/14

We continued our work with inequalities today by working with conditional statements again.  We had previously worked with if..then and converse statements.  The two new types of statements are the inverse and the contrapositive.  Both of these statements involve the word "not", and each still needs to be evaluated as either true or false.  We also went over how to work with venn diagrams and inequalities in order to make various conclusions.

Assignment:  conditionals WS  #2-16 evens +  section 6-2;  page 211;  WE 5-8, 11-12

Honors Geometry; 12/14

We turned in our chapter 6 review assignments today, as well as the chapter 6 entry task sheets.  The students then took the chapter 6 test in class.


Assignment:  extra credit puzzle option

Geometry; 12/13

We started chapter 6 today on inequalities in geometry.  We reviewed some concepts of algebra inequalities before taking a look at how to recognize inequalities in geometric drawings.  We also introduced the concept of what an inequality proof looks like.

Assignment:  section 6-1;  page 205;  CE  #1-19 all,  page 206;  WE  #1-8 all

Honors Geometry; 12/13

We spent some additional time today reviewing for the chapter 6 test tomorrow.  We went over the 1st review sheet from Friday, and then worked on the 2nd review sheet in class.  The answers to this second review sheet will be posted on this blogsite later this afternoon for the students to check their work.

Assignment:  Chapter 6 Review Sheet


Inequality Proofs;

1.  done together in class
2.  skip
3.             statements                                   reasons
     angle 1 < angle 3                                  given
     BA parallel to CD                                given
     AC > AD                                              given
     angle 3 congruent to angle 2                if lines ll, then AIA congruent
     angle 1 < angle 2                                  substitution
     BC > AC                                              longer side will be opposite larger angle
     BC > AD                                              subst./ transitive

4.    statements                                            reasons
     AC bisects angle BAD                         given
    angle 1 congruent to angle 2                 def. of bisect
     angle 3 = angle 1 + angle B                 ext. angle = sum of remote int. angles
    angle 3 > angle 1                                   property of inequality
    angle 3 > angle 2                                  substitution
    AD > CD                                              longer side will be opposite larger angle

Hinge Theorem worksheet

1.  angle 1 > angle 2
2.  angle 1 > angle 2
3.  ZB > XB
4.  HJ > KP
5.  angle 2 > angle 1
6.  angle 4 > angle 3
7.  angle PRS > angle PRQ
8.  FH > GE
9.  KP > KG
10.  x < 14
11.  x < 6
12.  x > 4
13.  x > 7
14.  x < 7
15.  x < 8
16.  x < 80
17.  x < 54/7
18.  x < 6
19.  x > 7
20.  x < 7
21.  x > 2

Proof

                  Statement                                      Reasons
      AB congruent to AD                               given
 angle ACD = angle B + angle BAC            ext. angle = sum of remote int. angles
angle ACD > angle B                                   property of inequality
angle B congruent to angle D                      if isos. triangle, then base angles congruent
angle ACD > angle D                                  substitution
AC < AD                                                      shorter side is opposite the smaller angle

Geometry; 12/12

School was cancelled due to snow!  Have a fun and safe day!

Honors Geometry; 12/12

School was cancelled due to snow!  Have a fun and safe day!

Our test will be postponed until Wednesday, 12/14

Geometry; 12/9

We went over the schedule today for the remaining days before Christmas break and how the semester finals fit into our schedule as well.  We then introduced the geometry scavenger hunt project that the students will be working on over the next few weeks.  We went through the packet together of how to put the project together and showed different examples of past student work.  The due date for this project is Monday, Jan. 9.  There is an extra credit option for turning in the finished project on Tuesday, Dec. 20.

Assignment:  none

Honors Geometry; 12/9

We had a two hour delay today, so the classes were only 25 minutes long.  We went over the homework assignment from last night and answered any questions that students had.  I then passed out the chapter 6 review sheet to the students as their assignment.  We will go over this assignment on Monday and do our final review for the chapter 6 test on Tuesday.

Assignment:  Chapter 6 review sheet

Geometry; 12/8

We turned in our review sheets and entry tasks sheets for Chapter 5 to begin the period today.  We then spent the remainder of the period taking the chapter 5 test.


Assignment:  extra credit puzzle option after the test

Honors Geometry; 12/8

We continued our work with inequalities in triangles today by going over how to handle inequalities between 2 triangles.  Whereas we worked with 5 different ways to prove triangles congruent, there are only 2 ways in which to work with triangles that are not the same size and shape.  The SAS and SSS inequality theorems are the concepts that we went over today.  These are both versions of the Hinge Theorem and its Converse.  We went over what these types of proofs look like before getting started on the assignment.


Assignment:  section 6-5;  page 230;  CE 1-8;  page 231-232;  WE  #1-11

Geometry; 12/7

We wrapped up our study of quadrilaterals today by going over the homework on trapezoids and answering any questions that the students had.  We then worked two other problems together using isosceles trapezoids.  One involved a calculation and one involved a proof.  These two review problems both will be helpful on tomorrow's test.  The rest of the period was spent working on the chapter 5 review sheet.

Assignment:  Chapter 5 review sheet

Review Sheet Answers

Trapezoids

1.  16
2.  17
3.  4
4.  8
5.  2
6.  78
7.  63, 117
8.  72, 108
9.  13
10.  15
11.  65, 115, 115
12.  angle B, angle CFE, angle DEF
13.  10, 15
14.  6, 8
15.  12
16.  24, 12
17.  2x, x = 1.2

Practice 20

1.  true
2.  false
3.  false
4.  true
5.  false
6.  angle Q
7.  RQ
8.  7.5
9.  3.7
10.  trapezoid
11.  6
12.  x = 3;  DF = 18
13.  angle GFE = 92;  angle DEF = 88
14.  rectangle
15.  angle WXY congruent to angle WZY
16.  WX parallel to ZY or WZ congruent to XY
17.  WX parallel to ZY or WZ congruent to XY
18.  ZP congruent to PX
19.  proof
                statements                                             reasons
   angle XWZ congruent to angle XYZ               given
  WX parallel to ZY                                             given
  angle WXZ congruent to angle XZY                if parallel lines, AIA congruent
  ZX congruent to ZX                                          reflexive
  triangle XWZ congruent to tri. ZYX                AAS
  WX congruent to ZY                                        CPCTC
  WXYZ is parallelogram                                   if one pair of opp. sides is
                                                                           congruent and parallel then
                                                                           parallel.

Quadrilaterals

1.  92,  88
2.  10
3.  x = 2
4.  x = 3
5.  AE = 13.4
6.  90
7.  angle HEF congruent to angle HGF
8.  EF parallel to HG or EH congruent to FG
9.  EF parallel to HG or EH congruent to FG
10.  I is midpoint of HF
11.  angle A ;  DE = 13
12.  BC = 24
13.  trapezoid
14.  median / midsegment
15.  isosceles trapezoid
16.  18
17.  80, 80
18.  rectangle
19.  rhombus
20.  isosceles trapezoid

Honors Geometry; 12/7

We continued our work with inequalities today by taking a look at how inequalities in a single triangle are handled.  We went over the inequality theorems involving both sides and angles, using information to rank the various angles and sides within a triangle.  Most of the ideas today are concepts that can be done mentally.  The problems then become a lot of drawing recognition that is involved to answer them.


Assignment:  section 6-4;  page 221;  CE  #1-12;  page 222-223;  WE  #1-16, 19

Geometry; 12/6

We continued our work with quadrilaterals today by going over how to solve problems involving trapezoids.  This shape has only one pair of sides that are parallel, but can be viewed as part of a triangle.  It has two sets of base angles and a midsegment that is parallel to both bases.  We went through 3-4 examples of calculation problems that can be done with trapezoids before the students got started on their homework.


Assignment:  section 5-5;  page 192-193;  WE  #1-18 all

Honors Geometry; 12/6

We continued our work with inequalities in geometry today by showing another way to work with inequality proofs.  We also introduced two new terms in how conditional statements are used in geometry.  The inverse and the contrapositive of statements were demonstrated as they relate to if..then statements in geometry.  We also went through how a venn diagram can be used to answer questions about inequalities in geometry.

Today was also the introduction of a end of semester project that will be due on Jan. 9.  I went over the explanation of the project with the students and showed them a few examples in class of what a finished product looks like.  We will be showing more examples in the days to come.


Assignment:  section 6-2;  page 210-212;  WE  #1-18 all

Geometry; 12/5

We continued our work with special parallelograms today by going over how to work with calculations involving rhombi, rectangles, and squares.  We went through 4-5 examples of how to perform calculations on these shapes using their unique properties.  The students then got started on their assignment towards the end of the period.


Assignment:  Special Parallelograms WS packet

Honors Geometry; 12/5

The students got back their chapter 5 tests today and had a chance to ask any questions that they may have had.  We then got started with the next unit of study today:  inequalities in geometry.  We reviewed some algebra inequalities that are important to know for this chapter and then began the process of showing the students what properties of inequalities look like in geometry.  We went through their first inequality proofs together to get them started.


Assignment:  section 6-1;  page 205;  CE  #1-19;  page 206;  WE  #1-8

Geometry; 12/2

The lesson today focused on the special properties of rectangles, rhombi, and squares.  These are all parallelograms with unique properties that can be helpful in working with different types of problems.  We went over each shape quickly to point out some of its unique properties as parallelograms before getting the students started on their assignment.

Assignment:  section 5-4;  page 186-187;  CE  #1-10 all,  WE  #1-10 all

Honors Geometry; 12/2

We turned in the entry tasks and the ch. 5 review sheet at the beginning of the period.  The rest of the time was spent taking the chapter 5 test in class.


Assignment:  extra credit puzzle option after the test

Geometry; 12/1

We collected our entry task sheets and the chapter 5 quiz review sheets to start off the period.  The students then spent the rest of the period taking the chapter 5 quiz.

Assignment:  extra credit puzzle option

Honors Geometry; 12/1

We continued our work with trapezoids today by going over how to work with isosceles trapezoids.  These have congruent legs, base angles, and diagonals.  We went through these properties and showed how they would be applied in a couple of different proof problems.  The students then got to work on their chapter 5 review sheet in class.


Assignment:  Chapter 5 review sheet

Chapter 5 Test tomorrow

Review Sheet Answers

Practice 20

1.  true
2.  false
3.  false
4.  true
5.  false
6.  angle Q
7.  RQ
8.  7.5
9.  3.7
10.  trapezoid
11.  6
12.  x = 3;  DF = 18
13.  angle GFE = 92;  angle DEF = 88
14.  rectangle
15.  angle WXY congruent to angle WZY
16.  WX parallel to ZY or WZ congruent to XY
17.  WX parallel to ZY or WZ congruent to XY
18.  ZP congruent to PX
19.  proof
                statements                                             reasons
   angle XWZ congruent to angle XYZ               given
  WX parallel to ZY                                             given
  angle WXZ congruent to angle XZY                if parallel lines, AIA congruent
  ZX congruent to ZX                                          reflexive
  triangle XWZ congruent to tri. ZYX                AAS
  WX congruent to ZY                                        CPCTC
  WXYZ is parallelogram                                   if one pair of opp. sides is
                                                                           congruent and parallel then
                                                                           parallel.

Quadrilaterals

1.  92,  88
2.  10
3.  x = 2
4.  x = 3
5.  AE = 13.4
6.  90
7.  angle HEF congruent to angle HGF
8.  EF parallel to HG or EH congruent to FG
9.  EF parallel to HG or EH congruent to FG
10.  I is midpoint of HF
11.  angle A ;  DE = 13
12.  BC = 24
13.  trapezoid
14.  median / midsegment
15.  isosceles trapezoid
16.  18
17.  80, 80
18.  rectangle
19.  rhombus
20.  isosceles trapezoid

Test 20;  Chapter 5

1.  triangle YWX
2.  angle XYZ
3.  110
4.  a. 30      b.  64
5.  a. 12      b. 6
6.  4
7.  rectangle
8.  rhombus
9.  parallelogram
10.  rectangle
11.  rhombus
12.  square
13.  sometimes
14.  sometimes
15.  never
16.  sometimes
17.  median ; midsegment
18.  a.  115;  b.  65
19.  7