This is organized by Topic but in the order covered in Discovering Geometry AS USED BY West Contra Costa Unifed School District.
Note: Some of the Worksheets where the question is in a text box DO NOT refresh well. To start over, a student should go back and click on the link again. Sometimes refreshing causes the answers to re-load but not the question! The newer ones like this do not have that problem.
* are links which I did not create and are on external sites.
Check out cool optical illusions and other related links to this chapter. (Interesting Islamic art article here)
Critical Geometry Vocabulary. Geometry Vocabulary Work
Practice vocabulary quiz here and actual quiz here.
Midpoint pactice here OR you can make up your own points.
Calculations for each problem will look as follows:
Points: (-6, 8) and (3, -4)
x = (-6+3)/2 , y = (8 + -4)/2
x = -3/2 , y = 4/2
Midpoint is (-1.5, 2)
check out protractor practice here *
Circle Basic Vocabulary Matching Quiz Practice: here
Circle Basic Vocabulary Matching Quiz: here
More vocabulary for entire course is at the bottom of the page.
Practice Figuring Out Patterns
EXAMPLE: We already discovered that for certain types of patterns, where the number advances by the same amount every time, that the function rule for this is jx + c where the coefficient j is the size of the step and the constant c is the amount needed to adjust the value to work for the first term. For instance:
Term n |
1 |
2 |
3 |
4 |
5 |
6 |
... |
n |
... |
200 |
Function f(n) |
8 |
11 |
14 |
17 |
20 |
23 |
... |
|
... |
|
The function is moving up by 3 each time so the function rule is 3n + something.
For term 1, f(1)=8, which means 3(1) + c = 8, which means c is 5.
Completing the table below looks like this:
Term n |
1 |
2 |
3 |
4 |
5 |
6 |
... |
n |
... |
200 |
Function f(n) |
8 |
11 |
14 |
17 |
20 |
23 |
... |
3n+5 |
... |
605 |
Introduction to Proof here
Bottom of page from above notes links to interactive examples here
Angle Addition Postulate and types of angle: link
Angle Addition Postulate with algebra component: link
See example of how to do work here.
Notes about parallel lines link
More practice on parallel lines link.
Practice Slope. For lines to be parallel, they must have the same slope.
Medium Coordinate Proofs on internet. Copy the Given. Draw a picture of the given (NEATLY!), Copy the statements and reasons.
Compass Links EACH OF THE WORKSHEETS, list the pages in the book where instruction can be found. In addition you can check out these video examples: creating a congruent segment bisecting a segment bisecting angles making congruent angles. creating a perpendicular from a point ON the line creating a perpendicular from a point NOT on the line creating parallel lines |
These are all sketchpad manipulatives:
See examples of quiz over constructions
Mr. Taylor's Geometry Assignments
May want to review protractor
Algebraic review of the Triangle 180 rule: Find the missing Angle
Manipulative showing why base angles are congruent: Link* Answer questions at bottom (takes a moment to load)
Chaser practice quiz. (Find the missing angles in large complex "chaser" picture - must know linear pair, vertical angles, base angles congruent, and triangle 180 rules to complete)
Same as above but quiz version: Here
Manipulative showing Triangle Inequality Theorem: here* Answer questions at bottom (takes a moment to load)
Really easy worksheet to check understanding: Here
Triangle Congruence Theorems (SSS, SAS...)
See examples of why these will always work here. (may take a minute to load)
Internet Practice for Determining if Two Triangles are congruent.
Chapter 4 mini Quiz practice: here (Contains Triangle Inequality plus "Side-Angle Inequality Conjecture")
Actual: this page
Manipulative showing external angles sum to 360: here* Answer questions at bottom (takes a moment to load)
Practice Quiz over interior and exterior angles of a polygon.
Quiz
Manipulative showing properties of kites: link* Answer questions at bottom (takes a moment to load)
Manipulative showing mid-segments of trapezoids: link* Answer questions at bottom (takes a moment to load)
Manipulative showing properties of parallelograms: link* Answer questions at bottom (takes a moment to load)
Practice Quiz for below is this
Polygons and Quadrilaterals Quiz
Another Practice Quiz on properties (Involves knowing that certain properties prove parallelograms - not in book?)
Another Quiz (matches to above Quiz)
See this movie about the area of rectangles/parallelograms/triangles. There is one small mistake in this movie. Can you find it?
Practice here for trapezoids then here for Rhombii and Parallelograms
Practice Squares, Rectangles, Parallelograms, Trapezoids, Triangles, and Kites quiz for below is this.
Quiz.
Circle Properties (area, circumference, radius, diameter) Using pi is this
Same using 3.14 to approximate is this
Internet practice with Surface Area and Volume
And Still More Practice here (includes cylinders)
Reviewing distance formula here* and here*
here. Right Triangle Rules.
SUGGESTED ASSIGNMENT: As you go, draw each pair of Triangles, Mark Congruent sides , and write down answer. Do 10-20 sets.
45-45-90 Triangle shortcuts. Draw a triangle for each problem (should look like 45-45-90 triangles!) Label all sides - given and found. Show work where necessary. Click Here. !
30-60-90 Triangle shortcuts. Draw a triangle for each problem (should look like 30-60-90 triangles!) Label all sides - given and found. Show work where necessary. Click Here.
Review shortcut for 45-45-90 and 30-60-90. See here for more examples.
Quiz over both types. Try now!
Word Problems using Pythagorean Theorem and Special Right Triangle Shortcuts. Draw a picture for each and show your work.
Another quiz is this.
Some Explanation: A right prism is a solid (3-dimensional) figure that has sides perpendicular to the "ground" and a top parallel to the ground. (see cool 3-d pictures here - Takes a moment to load). If you can calculate the area of the BASE, then multiplying it by the HEIGHT (sometimes called altitude) of the figure gives you the volume. Note the BASE and HEIGHT may mean something a little different than what you think of when talking about a 2-dimensional object. A few of the problems may have a parallelogram for a BASE. We haven't really discussed how to find the area for a parallelogram but it is really just base x height (because its tilted the height IS NOT the side). See this movie for a review of areas and for an explanation of the area of a parallelogram. |
For right prism volume, see here . This is also a good review of area of basic figures.
For right prims and cylinder volume, see here. Also a good review for area of a circle.
SUGGESTED ASSIGNMENT: For each of these you need to draw a picture of the BASE and show how you found the area. You should have 20 pictures and work total. (Many of you have not yet memorized the formula for area for rectangles, triangles, circles, and regular polygons. You need to memorize these formulas (bottom of worksheet) for the next test!).
See link under area for more Surface Area and Volume Practice
Volume including Spheres: here.
Proportion Word Problems. For each problem, set up a proportion WITH units and then solve.
Proving Similarity: Copy each picture, label it with measures, write down answers, and show checks when done. Quiz
The Sine Function Internet Worksheet. Create pictures and show work for each.
Introduction to the other two trigonometry functions: Cosine and Tangent. SEE THIS:
These shortcuts help us go from adjacent to hypotenuse or from opposite to adjacent.
Try the attached problems. Do 20 of them. Make a picture of each and copy down the work as you complete each exercise. Click here.
Short Cut Review (Longer Version)
Quiz over Trig functions (this is recorded in a database but if using in class you should show your teacher).
See this link on vocab and this link on area and lengths that are have been used in other chapters.
Finding measures of circle using Exact Measures (put pi in the answer) and using Approximate Measures (use 3.14 as pi)
Relationships of angles and arcs is here (this is recorded in a database but if using in class you should show your teacher).
More Arc/Angle rules is here.
Circle "Chaser" is here. Try Tougher Chaser
Still More Arc/Angle relationships are here.
BIG IDEAS:
|
practice on "Big Idea" concepts
Quizzes:
Part 1: Chords, Radius, and distance. Need all 10 but you get a second check!
Part 2: Circle Arcs and Angles, you only need 10 right on this page (Which means 18 as 8 are given to you already)
Any two chords that cross on the interior of a circle create similar triangles. Since similar triangles are proportional, if we know three of the four segments then we can use a proportion to find the other missing segment. See here.
Sectors and Arc Lengths. Try this. See example.
Not usually taught in much detail
Practice solving equations AND practice finding order pairs.
Finding ordered pairs (more - includes finding points on a circle)
Setting up slope-intercept form to find order pairs. For each problem, FIRST write down the the problem and rearrange into slope intercept form. SECOND, find the ordered pairs. Write these down (only need to show work for second step if you have problems finding right answer). Click here.
More Practice rearranging into slope intercept form. Also practice finding the common point (simultaneous solution) for two lines. Click here. For this exercise, you can either graph or solve by substitution. Ask for graph paper if you would like to solve by graphing.
See here for new recorded examples.
Quiz,
Try this factoring practice. Write down each problem and the answer. Submit when done.
At school and logged in, click here to find sketchup. Use File|Open to open each of the tutorials in order (Found at x:\google\tutorials). Read the instructions and do what it says to do in each one of the tabs. Show me 3 and 4 as you finish (you will need to do 1 & 2 in order to figure out 3 and 4). 5 & 6 are not required (but are fun!).
If at home, SKETCHUP can be downloaded.
Start exercises SK1 & 2. Instructions are found in the word document named CADGeometryIntro1 at google folder on the courses(X:) drive.
When done, you should have files Sk1 and Sk2 saved in your student folder, 2 sketches in notebook.
Continue with CADGeometryIntro2 and CADGeometryIntro3
MORE OF MY OLD LINKS MAY BE here. (Much of this is duplication although a lot of the Mini and Medium proofs are not included on this page).
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And these (may contain some of both lists). If you can explain all these, you have a good working knowledge of the language of geometry.
| angle | Intersection | bisector | diameter | radius |
| area | perimeter | volume | Surface Area | Square |
| Circle | chord | circumference | concentric circles | Arc |
| cone | cylinder | prism | sphere | pyramid |
| congruent | tangent | pi | rational number | hypotenuse |
| coordinates | Origin | slope | Distance Formula | Axes |
| Coplanar | collinear | rotation | Rotate | SOHCAHTOA |
| End point | Midpoint | Length | plane | Point |
| equilateral | isosceles | triangle | reflection | ray |
| integer | decimal | Irrational Number | fraction | percentage |
| n-gon | octagon | Krypto | decagon | hexagon |
| Parallel | Perpendicular | Skew | symmetry | Line |
| Parallelogram | Trapezoid | Rectangle | Rhombus | quadrilateral |
| placeholder (variable) | Right Triangle | altitude | Pythagorean Theorem | Segment |
| Polygon | vertex | side | regular polygon | tessellation |
| polyhedron | Face | edge | straightedge | compass |
| proof | given | radical sign | Square Root | protracter |
| Proportional | similar | scale | pentagon | Theorem |
A good group assignment is here.
Discuss creating vocabulary grids and assign groups and words (4 people, 4 words). Each person responsible for going home and researching meaning of all four words, examples, counter-examples and related information.
GGN - Home Version Available, In-Class Version is only when I'm around
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©2008 Michael Taylor
