Let’s start with what you know:
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
The simplest form for perimeter of a
parallelogram is: P = 2L + 2W (Can you apply the
distributive property to this?)
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.
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
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
(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?
- parallel (Remember this from slope in Algebra?)
- perpendicular (This was mentioned with slope in Algebra too.)
- points, lines, planes
- 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)
"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!