The Ithaca High School Geometry Blog

What did you think of the game in class today?

How do you think it could be improved?

Did you learn or re-learn anything?

Post a comment please.

Please see me as soon as possible (before school on Monday would be good, or contact me via email sooner) to schedule a time to make up the Chapter 3 test that you missed on Friday.  You may not take it during regular class time, but may make it up before school, during your lunch period or study hall, in your math lab or resource room, or after school.  Scheduling ahead maximizes both your time and mine. 

On Monday, we will dive right into Chapter 6:  Similarity.  To get you started, a simple definition of similarity is “same shape”.

The Chapter 3 Test will be given Friday, 10/19/07, rain or shine.  If you miss the opportunity given during the regularly scheduled class time, you will need to make it up on your own time (i.e., after school, during a study hall, during lunch).  You will not be able to take the test during class next week.  Tests not made up by Wednesday, October 24 will be recorded as zeroes.

Thanks to those students who were in class today.  I know that what we covered will help you do your construction project that will be assigned next week.  Plus, you were kind enough to help me eat my extra candy.

Tomorrow we start on parallel and perpendicular lines.

If you need more time to finish your Chapter 1 Test, YOU must find the time. You may come into any of my classes (1st, 3rd, 5th, 6th, 7th in H214, 2nd in H218, 4th and 8th in H211) if you have a study hall, CAL, or lunch, or come before school to H214. You have until the beginning of your Geometry class to complete it. (Problems, conflicts can be dealt with on an individual basis: see me ASAP.)

Today we began reviewing for the Chapter 1 Test, which is Wednesday. We did a vocabulary review worksheet then went to the computer lab to explore lines and segments on Geometer’s Sketchpad (GSP). What we did today on GSP will make using it later this year much easier. Tonight’s homework is a practice test.

Tomorrow we’ll check homework, go over the quiz you took on Friday, and then i’ll have a variety of worksheets that you can use to practice the skill and concepts which you need to work on the most prior to the test.

And one more thing: Happy Birthday to T.V. in 6th period.

Today we summarized and reviewed the midpoint and distance formulas.

Tomorrow there will be a quiz covering lessons 1.1 thru 1.3, including points, lines, and planes and how they are labeled, as well as the midpoint and distance formulas. The quiz should not take more than half the period.

To prepare, review the vocabulary words, skim through the lessons in the book looking particularly at diagrams, highlighted words, and items in green boxes, and memorize the distance and midpoint formulas.

Topics covered in class today included the derivations of the midpoint formula and the distance formula from one dimension to two.

The midpoint formula: it’s a point, so it must have two values, one for the x term and one for the y term, which are separated by a comma, and the point is enclosed within parentheses. Two get the x term, add the x terms of the endpoints of the segment and average them, or divide by two. Do the same thing for the y values.

( (x1 +x2)/2) , (y1 + y2)/2 )

The distance formula is based on the Pythagorean Theorem, which can often be used in its place to determine the length of a segment–all you have to be able to do is determine a right triangle. For the formula, you must determine the difference between the x values, which is like finding the a for the Pythagorean Theorem, and also determine the difference between the y values, which is like finding the b. Square each value, add them together, then take the square root of the sum.

d = sqrt( (x2 – x1) ^2 + (y2 – y1) ^2 )

Because we use this a lot in geometry, you need to memorize and learn this now, instead of waiting until June when you have your final exam.

You must be familiar with simplifying radical numbers also. Only a few combinations of numbers fit the Pythagorean Theorem so that all three numbers are whole numbers. These combinations are called Pythagorean Triples, and here is an address of a list of Pythagorean Triples: http://planetmath.org/encyclopedia/LeastCoprimePythagoreanTriplets.html . You should memorize this list. Or maybe at least the first half dozen on it.

Some key ideas from today’s class:

Distance is always positive, so to find the distance between two points on a number line, find their difference, then take the absolute value.

The midpoint is half way between the two end points of a segment. Another way to think of the midpoint is that it is the average of the two endpoints. To find the midpoint on a number line, add the endpoints and divide by two.

Distance: subtract, then absolute value
Midpoint: add, then divide by two

We’ll be using square roots to find distances once we get to two-dimensions tomorrow, so you need to know your squares and square roots. To learn them, start by making a list of numbers and their squares. Look for patterns. Then make flash cards and quiz yourself. Here is a website from which you could download a list of the first hundred square numbers, or more: http://naturalnumbers.org/psquares.html

Check out yesterday’s notes for additional ways to learn and earn extra points and improve your grade.

Are you fascinated by Square Numbers? Here is an address of a website that will tell you more than you ever wanted to know about square numbers: http://mathworld.wolfram.com/SquareNumber.html

Today we discussed (among other things) the first two postulates, found in Lesson 1.2: The Ruler Postulate and the Segment Addition Postulate. Remember that a postulate is a rule that we accept without proof, while a theorem is rule which we are able to prove.

The Ruler Postulate basically says that we can put a name or value to every point on a number line, and that between any two points that you can name, I can name another.

The Segment Addition Postulate says that you can add two segments on the same line together to get another segment, and that the length of the combined segment is equal to the sum of the lengths of the two smaller segments.

We’ll use the ideas of the Segment Addition Postulate tomorrow when we discuss MIDPOINT and DISTANCE on a line segment.

Double extra credit for the first three students who make a comment to this post who haven’t made a comment to today’s Assignments post.