The Ithaca High School Geometry Blog

Assignment for Tuesday, September 18, 2007
Due Wednesday, 9/19/07

Vocabulary Assignment #2 worksheet

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.

Assignment for Monday, September 17, 2007
Due Tuesday, 9/18/07

p. 19 #4, 9, 15, 18, 19, 24, 26, 32, 33, 45
p. 139 #15-23 odd

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.

Assignment for Friday, September 14, 2007
Due Monday, 9/17/07

p. 19 #1, 7, 10, 12, 17, 21, 25, 31
p. 139 #10, 11, 12, 13, 19

Expect a pop quiz on Monday. Two questions will probably be to state the Midpoint Formula and the Distance Formula (for two dimensions). Other questions might be to find the midpoint and find the distance of line segments.

There will be a Quiz on Tuesday covering lessons 1.1 thru 1.3.

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

Assignment for Thursday, September 13, 2007
Due Friday, 9/14/07

p. 875 #6, 17, 28
p. 19 #5, 8, 11, 14, 35, 39
p. 12 #18, 19, 24

Also, study five minutes for tomorrow’s pop quiz on squares of 1 through 30.

Did you check out yesterday’s class notes?

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.

Assignment for Wednesday, September 12, 2007
Due Thursday, 9/13/07

p. 875 #5, 14, 18, 27
p. 12 #1, 6, 10, 12, 16, 17, 21, 23, 28

First three students to post a comment earn extra credit (tell your friends).

Assignment for Tuesday, September 11, 2007
Due Wednesday, 9/12/07

P. 5 #1, 3, 5, 6, 9, 11, 17, 30, 33, 35, *46
(*46 means problem #46 is a challenge problem. Please try it, but if you cannot figure it out that’s okay, i won’t count it against you.)
Note that most of these problems are odd-numbered, which means that the answers are in the back of the book. Please check your answers, then come to class tomorrow with your questions.
One good way to remember which problems you need help with is to mark them on your homework. Just put “???” next to the problem number, or circle the problem number, or put a star beside it. This will make it easier for you to see which ones you need to ask about.