Coordinate Geometry Independent Study

Outcomes:

E5 apply inductive reasoning to make conjectures in geometric situations

D1 develop and apply formulas for distance and midpoint

E7 investigate and make and prove conjectures associated with chord properties of circles

E11 write proofs using various axiomatic systems and assess the validity of deductive arguments

E4 apply properties of circles

E15adv solve problems involving the equations and characteristics of circles and ellipses

1. Word list:

Be sure you fully understand the meanings of the following words. / If you need clarification, check these sites or a math dictionary:
Altitude
Angle
Chord
Congruent
Converse
Diameter
Equidistant
Equilateral
Isosceles triangle / Line
Line segment
Polygon
Quadrilateral
Radius
Ray
Rhombus
Scalene triangle
Trapezoid / http://www.teachers.ash.org.au/jeather/maths/dictionary.html dynamic, fun, a little childish
http://thesaurus.maths.org/ very thorough – provides background
http://www.infomath.com/html/geometryglossary1.asp glossary of geometry terms
http://library.thinkquest.org/2647/geometry/glossary.htm terms and symbols
http://www.mathwords.com/a/altitude_triangle.htm includes diagrams

2. Developing Formulas: Use the websites and/or the text to help you understand and use the formulas. Then do the indicated questions from the text and check your answers (see text)

Websites: / Text:
Slope:
http://www.purplemath.com/modules/slope.htm examine the entire page
http://mathforum.org/cgraph/cslope/ very thorough
http://www.math.com/school/subject2/lessons/S2U4L2GL.html
http://cs.selu.edu/~rbyrd/math/slope/ simple, basic, self test
http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=87 interactive, steps for calculating slope. Click on Launch Gizmo. Click on Exploration Guide for directions if you need them.
http://math.usask.ca/~maclean/101/Review/Printables/BW/Lines.pdf slopes and equations of lines examples
my GSP activity / Investigation 3
Page 222 – 223
Practice: Page 222 #1, 3 on graph paper
Distance formula:
http://www.purplemath.com/modules/distform.htm uses Pythagorean theorem; gives examples
http://www.learner.org/channel/courses/learningmath/geometry/session6/part_c/distance.html from Pythagoras to the distance formula
http://cs.selu.edu/~rbyrd/math/distance/ simple, basic, self test
http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=183
click on Launch Gizmo / Focus C
Page 224 - 226
Practice: Page 226 # 11, 12 on graph paper
Midpoint:
http://www.mathsnet.net/dynamic/jsp6.html what is meant by midpoint?
http://www.purplemath.com/modules/midpoint.htm look at the examples showing how it is used
http://cs.selu.edu/~rbyrd/math/midpoint/ simple, basic, self test
Practice: Page 230 #28, 29 on graph paper

Summary of formulas

Slope / Midpoint / Distance
= / = / =
=
Parallel
(use || for “is parallel to”)
Perpendicular
(use for “is perpendicular to”) / If two lines are parallel, their slopes are equal.
If two lines are perpendicular their slopes are negative reciprocals. The product of the slopes is -1.

Equation of a line:

Slope y-intercept form / Slope Point Form
If m = slope and b = y-intercept then the equation is
y = mx + b / If (x1, y1) is a point on the line and m = slope then the equation is
y – y1 = m(x - x1)

Necessary and sufficient conditions:

Trapezoid:
·  One pair of opposite sides parallel
/
Parallelogram:
·  Two pairs of parallel sides
-OR-
·  One pair of parallel and congruent sides /
Rhombus:
·  Four sides congruent
-OR-
·  Parallelogram with one pair of adjacent sides congruent /
Rectangle:
·  Two pairs of congruent sides and one 90⁰ angle
-OR-
·  A parallelogram with one 90⁰ angle /
Square:
·  Rhombus with one 90⁰ angle
-OR-
·  Rectangle with one pair of adjacent sides congruent /
Kite:
·  Two pairs of adjacent sides congruent /


Classification of Quadrilaterals