## Saturday, July 17, 2010

### PREPARING FOR THE NEXT LEVEL OF MATH: GEOMETRY

The good news about Geometry is that you’ve studied most of it before. The best news for a visual learner is that many of the theorems can be depicted through drawings. Of course the downside for some is the need for precision in this branch of math, but just a little attention to detail can make even this a minor hurdle easily scaled.

AREA

All of these are parallelograms: Length times width
A = LW

Take any parallelogram and draw a diagonal... and you have 2 identical triangles:
Area is 1/2 the area of the parallelogram
A = 1/2 LW

Here’s a circle.
Area = π (r) squared

PERIMETER

The simplest form for perimeter of a
parallelogram is: P = 2L + 2W (Can you apply the
distributive property to this?
)

CIRCUMFERENCE
Must be a circle: (2πr). Check out the similarity between area and circumference.

In high school Geometry, you'll also learn area of any polygon.

Pythagorean Theorem

I've extolled the virtues of the Phythagorean Theorem in previous blogs. Know it and look for ways to use it in Geometry, Trigonometry, and Calculus.

Here are a few common knowledge items you will want to remember:

1. Sum of the interior angles:
• triangle = 180
• parallelogram = 360
2. Degrees in a circle = 360

3. Triangle Categories
• equilateral - all sides equal
• equiangular - all angles equal
• isosceles - 2 sides equal (and 2 angles equal)
• scalene - no sides or angles equal
• obtuse - one angle bigger than 90 degrees
• acute - all angles smaller than 90 degrees
• right - one 90 degree angle
4. Two points determine a line.
(The shortest distance between two points is a straight line.)

5. Three points determine a plane.
(So does one line and another point........why?)
(So do two parallel lines..........................why?)

6. Vocabulary.......remember these?
• skew
• parallel (Remember this from slope in Algebra?)
• perpendicular (This was mentioned with slope in Algebra too.)
• points, lines, planes
• intersection
• segment
• ray
• endpoint
• right angle
• acute angle
• obtuse angle
• complementary angles (Can you distinguish this "complementary" from "complimentary" elsewhere?)
• supplementary angles
• triangle, quadrilateral, pentagon, hexagon, septagon, octagon, nonagon, decagon, n-gon
• radius, diameter, tangent, secant, chord, arc (Relate these to the circle.)
• altitude of a triangle
• diagonal (in any polygon)
• similar
• congruent
In Honors Geometry, you'll be immediately working with postulates, theorems and axioms as they relate to two-column PROOF. Think of it as giving the reason for taking a computation step. Learn the theorems as they occur in the chapters and try to hear the music, the rhythm of each. "Two points determine a line" is one of them. Here's another:

"Given two parallel lines and a transversal, alternate interior angles are congruent." Eventually you'll be able to abbreviate this as AIA, but learn the whole rule first.

General tips for Geometry

Employ your artistic, creative side. Visualize or use the rhythm of music. Try drawing figures with your non-dominant hand. And DO draw the figures!