Mid-Chapter Review

We started the class off by reviewing a few questions from our previous assignment. We also reviewed that proofs need to be based on facts. For example if two parallel lines are cut by a transversal, and we need to prove that angle  d is 73°, we would say that angle c is 107° because it is the corresponding angle to the one labeled 107°. Next we would say that since angle d is supplementary to c, and c is 107° therefore angle d is 73° because supplementary angles must add up to 180°.

  We then got into groups where each group was assigned a question from the mid-chapter review from pg. 84. We were to answer the question we were given, and then show and explain our work on the overhead projector. Since it was a half day and we did not have time for anything else, we dispersed joyfully when the lunch bell rang. A diagram has been provided to accurately represent the level of joy.
The next to post in the blog will be Tanner.

Angles Formed by Parallel Lines

We started off class by looking over our Chapter 2 diagnostic work sheet and correcting a classmates to show Mr.Banow our knowledge in this unit so far.

Converse is a statement that is formed by switching the premise and the conclusion of another statement.

Next we worked on page 72 which is reviewing parallel lines and transversals.

We reviewed what Alternate Interior and Exterior angles were.

Alternate interior angles are two non-adjacent interior angles on opposite sides of a transversal. Which is angles 3,6 and 4,5.

Alternate exterior angles are two exterior angles formed between two lines and a transversal, on opposite sides of the transversal. Which is angles 1,8 and 2,7.

We also reviewed what Supplementary and Complementary angles were. Two angles are Supplementary angles if they add up to 180 degrees. These two angles (140 degrees and 40 degrees) are Supplementary Angles, because they add up to 180 degrees. These two angles (40 degrees and 50 degrees) are Complementary Angles, because they add up to 90 degrees.

The next person to blog will be, AARON. :)

OH YAH, and don't forget to bring a compass, protractor and ruler ASAP.

Exploring Parallel Lines

In our last class we started chapter 2. We learned about identifying relationships among the measures of angles formed by intersecting line. We learned about transversall lines which is a line that intersects two or more other lines at distinct points. We learned about exterior angles which is the angle that is formed by a side of a polygon and the extension of an adjacent side.  We learned about interior angles which are any angles formed by a transversal and two parallel lines that lie inside the parallel lines. We learned about corresponding angles which is one interior angle and one exterior angle that are a non-adjacent and on the same side of the transveral. Converse is a statement that is formed by switching the premise and the conclusion of another statement. A key summary to follow is when a transversal intersects a pair of parallel lines, the corresponding angles that are formed by each parallel line and the transversal are equal. things you need to know is when a transversal intersects a pair of non-parallel lines, the corresponding angles are not equal. There are also other relationships among the measure of the eight angles formed when a transversal intersects two parallel lines. To do all of this you will need some materials such as a dynamic gemoetric software or a ruler and protractor.

Our class did a hand out assignment on this and then we went over all the answers as a class and i believe it went very well because our class is very smart.

Next will be michelle :)

properties of angles and triangles. :)

yesterday (thursday) mr banow was not present. therefore we had Mrs. Smith as a sub.
we worked on a sheet to test our knowledge about triangles and angles and then worked on a dog activity on page 68. Most groups failed at the objective of making a dog using polygons.
this is all.
peeace.
next is............. cody. :)

Analyzing Puzzles and Games

On Friday, in class we discussed more about analyzing puzzles and games in section 1.7. the goal of this section was to determine, explain, and verify a reasoning strategy to solve a puzzle or to win a game. We looked at example one which was on using reasoning to determine possible winning plays in a game of darts. example two was on using deductive and inductive reasoning to determine a winning strategy while playing the toothpick game. We discussed Alice's solution into winning the game every time. Alice discovered in order to win she must leave Nadine 3, 6, 9, 15, or 18 toothpicks. This strategy will work and Alice will win every time and long as she goes first.
In summary: Both inductive and deductive reasoning can be useful for determining a strategy to solve a puzzle or win a game. Inductive reasoning is useful when analyzing games and puzzles that require recognizing patterns or creating a particular order. Deductive reasoning is useful when analyzing games and puzzles that require inquiry and discovery to complete.

we ended class with an assignment on page 55. #5,6,7,9,11

Next post will be from Amy! yay!

1.6 Recap & 1.7: Analyzing Puzzles and Games

A synopsis of the day:

We were given ample time to thoroughly complete and review our previous assignment. This section helped improve our ability to decide whether to use inductive, deductive, or both types of reasoning on certain problems.

An example of one of the problems in our assignment is as follows:

Use inductive reasoning to determine the number of diagonals that can be drawn in a decagon.

Since we are limited to inductive reasoning, we must first illustrate a specific polygon and then form a pattern, of which can be applicable for a plausible conjecture.

Just look at that craftsmanship.

We can determine that a pentagon will have 5 diagonals. If we looked at a picture of a hexagon, we would see that it will have 9 diagonals; a heptagon, 14. We notice that as the number of sides increase, we increase the addend by an increment of 1 each time. If we follow that pattern, then our conjecture would have to be that a decagon will have 35 diagonals.

After reviewing the assignment, we proceeded to briefly start section 1.7. This section shows that finding a strategy to solve a puzzle or win a game can be achieved via both inductive and deductive reasoning.

We then investigated the math by trying to solve a leapfrog problem. The lowest amount of moves needed to solve the game with 3 pieces on each side was 15; with 2 pieces 8; and with 5 pieces 24.

That was the conclusion of our lesson. Our assignment for Friday is pg. 55 (5, 6, 7, 9, 11).

The next person writing the blog shall be Taryn.

Reasoning To Solve Problems

Summary:
To improve problem solving it would help to understand inductive and deductive reasoning. Deductive reasoning is based on facts that lead to a logical explanation, where as inductive reasoning is based on simple patterns to try and solve the problem.

Example of a deductive problem:
Mammals have hair. Dogs are mammals. So therefore, dogs have hair.

Conclusion:
Based on the statement, the answer is deductive because it demonstrates proof in the original statement.
Mammals have hair. (Which is all mammals, not just dogs)
Dogs are mammals. (Mammals have hair)
So we can come to the conclusion that, yes, all dogs have hair because there are mammals. There is proof stated, so the answer cannot be inductive, the statement is deductive.

- Next is Alex :)

SEPT 13

proof that is not valid

summary:
a single error in reasoningwill break down the logical argument of a deductive proof. this will result in an invalid conclusion, of a conclusion that is not supported buy the proof.
trying to divide by 0 will always cause a proof to be wrong, leading to an conclusion that is also wrong. also try avoid circular reasoning. when you write a proof try to keep is that it don't take a rocket scientist to make sense of it.

an example of to days work:
identify the error: all squares have 4 right angels. Quadrilateral PQRS has 4 right angels. therefore, PQRS is a square.

answer: not true quadrilateral PQRS could be a rectangle

Next is Joel

Sup

nothing, you?