Thursday, October 19, 2017

Geometry; 10/19

We got started on the 2nd half of the chapter today by starting work on an inductive reasoning project that deals with polygons.  We will be working on this over the next couple of days.  Today was focused on determining some patterns among the numbers involving the number of sides a polygon has and the sum of its interior and exterior angles.



Assignment:  Inductive Reasoning Project;  page 1 only

Honors Geometry; 10/19

We wrapped up chapter 3 today by taking a more specific look at inductive reasoning.  We went through several examples of number patterns and various described scenarios in which the students needed to decide which kind of reasoning - deductive or inductive - was being used to make decisions.  The students then got started on their assignment.


Assignment:  section 3-6;  page 107-108;  CE 1-5;  WE 1-17;   p. 110;  #1-15 all

Wednesday, October 18, 2017

Geometry; 10/18

The students turned in their chapter 3 quiz review sheets to start the period.  The rest of the period was spent taking the chapter 3 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 10/18

We continued our work with polygons today by taking a look at other types of polygons  (not triangles).  We used our knowledge gained from the inductive reasoning project to work with both interior and exterior angles of polygons.  We went through a few practice examples together before getting started on the assignment.


Assignment:  section 3-5;  page 104-105;  WE 1-17, 21, 22   (skip #7)

Tuesday, October 17, 2017

Geometry; 10/17

We spent time today reviewing for our chapter 3 quiz tomorrow.  With partners, the students worked through 8-10 review problems together that are indicative of what they will see tomorrow on the quiz.  They also worked on a review sheet towards the end of the period that will help prepare them for the quiz.  The answers to the review sheet appear below.


Assignment:  Chapter 3 quiz review sheet


Properties of Parallel Lines

1.  skip
2.  skip
3.  AIA
4.  corresponding angles
5.  SSI angles
6.  none
7.  angles 1, 13, and 15
8.  angles 2, 4, and 6
9.  angles 1, 3, 5, 7, 11, 13, 15
10.  angles 2, 4, 6, 8, 10, 12, 14, 16
11.  angle 11 = 55;  angle 15 = 55
12.  angle 4 = y;  angle 3 = 180 - y
13.  x = 70;  y = 90
14.  x = 15;  y = 40

Proving Lines Parallel

1.  GA parallel to EC
2.  GE parallel to AD
3.  GB parallel to ED
4.  none
5.  GB parallel to ED
6.  GB parallel to ED
7.  AD parallel to GE
8.  GB parallel to ED
9.  GE parallel to AD
10.  x = 9;  y = 22
11.  x = 21;  y = 17
12.   proof steps
        1.                                                1.  given
        2.                                                 2.  def. of angle bisector
        3.  angle 1 congruent angle 2      3.
        4.                                                 4.  transitive / subst.
        5.                                                 5.  if AIA congruent, then lines parallel



Solving for x:

19.  x = 4
20.  x = 7
21.  x = 8
22.  x = -7
23.  x = 9
24.  x = 5
25.  x = -6;  angle is 90
26.  x = 4;  angle is 85
27.  x = 10;  angle is 60
28.  x = -9;  angle is 80


Proof #4

statements                                    reasons
l parallel to m                               given
angle 1 cong. angle 2                    given
angle 1 cong. angle 4                   if lines parallel, Corr. angles congruent
angle 2 cong. angle 4                   substitution.


Proof #5

statements                                     reasons
angle 1 cong. angle 2                    given
angle 2 cong. angle 4                    given
angle 1 cong. angle 4                    subst.
line l parallel to line m                 if corr. angles congruent, then lines parallel

Honors Geometry; 10/17

We spent a little time wrapping up the inductive reasoning project before going on to our lesson for today.  Today's topic centered on how to work with triangles with both words and calculations.  We went over several vocab words pertaining to the ways in which triangles are classified.  We then used the triangle sum theorem (all angles sum to 180) to determine a variety of calculation and drawing problems.  The students then got started on their homework.


Assignment:  section 3-4;  page 97-99;  WE 1-20, 26, 28, 30

Monday, October 16, 2017

Geometry; 10/16

We continued our work with parallel lines today by taking a look at how to prove lines parallel.  We use our three angle pairs to work through a variety of drawings in order to determine if lines were parallel or not.  The students then got started on their assignment.

Assignment:    Section 3-3;  page 86;  CE 1-11;  page 87;  WE 1-19