Class Summary- Wednesday, December 8th

 

Lesson 6-5-

 
1. Definition of a Trapezoid: It's a quadrilateral with exactly one pair of parallel sides.
 
(Notes: If it has one pair of parallel side that ate also congruent, it is a parallelogram - Theorem 6-8-  and not a trapezoid)

 
2. Bases- the parallel sides (of a trapezoid)
    Legs- The other sides (which are not parallel)
 
3. In a trapezoid, consecutive angles, one from each base, are congruent

4. Two kinds of Trapezoids:
 
Right Trapezoid- has one right angle.

                             - The consecutive angle on the same leg is also right because of Theorem 3-4 (if: the transversal of perpendicular lines is perpendicular to one parallel line, then: it is also perpendicular to the other parallel line.)

Iscosceles Trapezoid- has congruent legs.

5. Median of a Trapezoid: a segment whos endpoints are the midpoints of the legs.

6. Theorems:

T 6-14- if: it is an isosceles trapezoid,

               then: both pairs of base angles are congruent.

T 6-15- if: it is an isosceles trapezoid,

               then: the diagonals are congruent.  (Notes: that doesn't mean they bisect each other.) 

T 6-16- (if) the median of a trapezoid is:

               (then) parallel to the bases,

               AND

               (then) its measure is one-half the sum of the measures of the bases.

The Homework for tomorrow is: Page 325# 16-37 all. 

Also, you have to post your opinion about the presentation to the 1st graders (a paragraph).

1st Grade Presentation Reflection =)

Well, I thought the presentation for the first graders worked well! All three groups got the children entertained and I believe all the first graders learned a little bit. I also felt that some of them really wanted us to clarify what exactly was a parallelogram and even though we didn’t I think they understood it more or less. The entire class collaborated, not only the first graders – that were silent and paying attention – but also the ninth graders for when one group was presenting the others were not making a mess. Furthermore, we were able to deal with the computer that didn’t work at first, what showed that all groups were ready since the second groups presented before the first. In addition, the experience of teaching the first graders was really nice and I believe the first graders themselves thought so too.

1st grade presentation reflection

Overall, the first grade presentations worked out really well. All the kids cooperated more than i would expect, and that should be by the fact that all of them were interacting. They really enjoyed the part of the activities, and my group heard some remarks like "this is too easy", therefore making us challenge them even more by putting the tangram togheter only with the shape's final form shadow only, without the outlines. As that was proven to be too hard, we started challenging them to work in a group and try forming one of the shapes displayed on the television screen. While they were working we started giving them tips and also repeating the Tangram rules: All shapes used, no overlapping and all of the pieces inside the shape's shadow. After they did aboput three of those our time was up. Overall this was a very good experience, since some kids were not cooperating and some were fighting for the tangram pieces (Each kid was given one piece), but that is normal. In the end i think they learned about them in a good way.

Posting for Friday the 5th

Sorry, It's extremely late.

Remember:

• This year postings are only graded for participation, but next year they will be graded. Diagrams and equations are NECESSARY


• Tuesday 9B will present at Jo Mannings 1st grade
  
  

We started class by correcting homework on page 316 and 317

Remember the quadratic equation that we have been using: **Memorize it! There will be a question in the test!!

Exercise 34 and 37 in pg 317 can be solved only by the slope formula. There is no need to do the distance formula. Do first the slope of sides, then the slope of the diagonals. If it is a rectangle and a rhombus, you know it is a square.


Test Firday!!

Giulia

Today's class summary 08/12

1- Today's class started over theorem 6-13 that said:

if: it is a rhombus

then: each diagonal bisects a pair of opposite angles

2- After that we went over the homework (p.317 #4 and 21-47), which was kind of easy for the people that actually did it, with no provings ;D. The question that most people had doubts was #33, because we had to use the quadratic formula(you can see it in Jenni's post). Also, for numbers 34-37, you could solve it using only the idea of slopes without the distance formulas.

Obs. Mrs. Saatkamp won't accept any graphing on quizzes and tests, only algebra.

3- After the homework, we started the lesson 6-5 that is about trapezoids:

Trapezoid's definition: It's a quadrilateral with exactly one pair of opposite sides parallel.

There are two types of trapezoids: Right Trapezoid and Isosceles Trapezoid

Right Trapezoid: It has exactly two right angles

Isosceles: Its legs are congruent


4- After looking over the trapezoids, we went over 3 theorems: theorem 6-14, theorem 6-15 and theorem 6-16.

theorem 6-14: If it is an isosceles trapezoid, then both pairs of bs angles are congruent

theorem 6-15: If it is an isosceles trapezoid, then the diagonals are congruent. Obs. the diagonals don't bisect each other

theorem 6-16: If it is a trapezoid, then the median is the sum of both bases divided by two.

Homework is only due on thursday because tomorrow we are going to work on the projects and on wednesday we are going to present for the little kids. Hw: p.325 #16-37 except for 36.

PS. 33-35 requires algebra

guilherme bessa

Today we started correct the homework from page 301, #15-32 all and page 310, #15-38 all. After Ms. Saatkamp explain soome questions in the homework, and we started learning about two other type of quadrilateral, Rhombi  (rhombus), and square.

And  some other theorem 

Theorem 6-11:   If It´s a rhombus, them the diagonals are perpendicular

Theorem 6-12: if a parallelogram has perpendicular diagonals, them it's a rhombus

the square don't heve a expecific theorem, but it have a definition: 

Square definition

it's a quadrilateral with four sides and four right angles 

Class Summary 4/12/08 by Guilherme

Today we started things off by going over the homework from page 301, #15-32 all. After Ms. Saatkamp corrected some diagram questions in the homework, we started learning about another type of quadrilateral, Rectangles.

Rectangles

Definition: A quadrilateral with four right angles.
There are two theorems on chapter 16 regarding rectangles especifically, and those are:

Theorem 6-9: If a parallelogram is a rectangle then it's diagonals are congruent.
Explanation: For example, if a parallelogram being a rectangle is given as information then it can be stated than all the diagonal lines in that rectangle is congruent, or equal to each other.

Theorem 6-10: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Explanation: A parallelogram can be considered a rectangle if its diagonals are congruent.


After we got over Rectangles we moved on to Rhombi (Rhombus).

Rhombus

Definition: It's a quadrilateral with all sides congruent.
Unlike Rectangles, they have three theorems especifically for them, and those are:

Theorem 6-11: If it is a rhombus then the diagonals are perpendicular.
Explanation: If the figure given is rhombus then it can be said that its diagonals are perpendicular to each other, eventually forming 90 degree angles.

Theorem 6-12: If a parallelogram has perpendicular diagonals then it is a rhombus.
Explanation: If the figure given is said to be a parallelogram and if that parallelogram has perpendicular diagonals then it is correct to assume that the figure is a rhombus.

Theorem 6-13: If it is a rhombus then each diagonals bisect a pair of opposite angles.
Explanation: If the rhombus is given then its diagonals will bisect (pass through the middle) of a pair (2) of opposite angles in that rhombus.

Then went on to Squares, however we didn't have any theorems on them. Instead, Ms. Saatkamp drew us a very helpful diagram about Quadrilaterals.

PARALLELOGRAMS-

RECTANGLES - RHOMBI


SQUARES


This basically states then all the properties used to identify Parallelograms can also be used to identify Rectangles and Rhombi, apart from their own. Squares are the Quadrilaterals that can be identified with any of the properties used on all the three of the Quadrilaterals above.

Finally we finished it off by copying the homework pages

Page 316 #4
Page 317 #'s 21 through 47 ALL