TI-92 Geometry Tour
TI-92 Geometry Tour
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The following tutorials and reference material are to help you learn geometry through a dynamic environment. This means you can interact and manipulate with geometric objects without having to redraw them. The geometry program on the TI-92 calculator will accompany your textbook, UCSMP Geometry, and will be used throughout the school year to help you conjecture and learn mathematical ideas and principles.
The lessons in this guide are established through a building process. In each subsequent lesson, you will be asked to recall how you created an object from a previous activity. Therefore, it might be difficult to jump around between lessons. If you work through all of the lessons, and forget how to create something, use the Index in the back to help guide you to the exploration where it was first explained. Keep this handout for future reference.
TABLE OF CONTENTS
|EXPLORATION |TITLE |PAGE(S) |
| | | |
|0-1 |Hey, my screen isn't dark enough (too light)! |5 |
|0-2 |Oops! I pressed the wrong key |5 |
|0-3 |Create a new folder |5 |
|0-4 |Create a new document |5-6 |
|0-5 |Create, label, and move points |6-7 |
|0-6 |Correct an error or clear the screen |7-8 |
|0-7 |Create two intersecting lines |8 |
|0-8 |Create, measure, and change a circle |9-10 |
|0-9 |Create, measure, and change an angle |10 |
|0-10 |Create, measure, and change a triangle |11 |
| | | |
|1-3 |Equation of lines |12-13 |
|1-5 |Drawing in perspective |13-14 |
| | | |
|2-4 |Midpoints |15 |
|2-7 |Triangle inequality |15-16 |
|2-8 |Conjectures ................................................................ |16-17 |
| | | |
|3-1 |Angle bisector |18 |
|3-2 |Rotations ................................................................... |19 |
|3-3 |Vertical angles |20 |
|3-6 |Slope and parallel lines |20-21 |
|3-7 |Perpendicular lines |22 |
|3-8 |Perpendicular bisector |22-23 |
|3-8P |Find the hidden treasure |23-24 |
| | | |
|4-1 |Reflecting points |24 |
|4-2 |Reflecting figures in a coordinate plane |25 |
|4-3 |Reflections and minimum distance |26-27 |
|4-4 |Translations: Composing reflections over parallel lines |27-28 |
|4-5 |Rotations: Composing reflections over intersecting lines |28-29 |
|4-6 |Translations and vectors |29-30 |
|4-7 |Glide reflections |30 |
| | | |
|5-2 |Congruence and equality |31 |
|5-4 |Alternate interior angles |31 |
|5-5 |Perpendicular bisector theorem |32 |
|5-5P |Capture the flag |32-33 |
|5-7 |Sum of angles in a polygon |33-34 |
| | | |
|6-1 |Reflection-symmetric figures |34-35 |
|6-2 |Isosceles and equilateral triangles |35-36 |
|6-2P |Shark attack |36-37 |
|6-3 |Constructing parallelograms |37-38 |
|6-4 |Constructing a kite |38-39 |
|6-5 |Constructing a trapezoid |39-40 |
|6-M |Mystery quadrilaterals |40-42 |
|6-6 |Rotation symmetry |43-44 |
|6-7 |Regular polygons |44-45 |
TABLE OF CONTENTS (CONTINUED)
|EXPLORATION |TITLE |PAGE(S) |
| | | |
|7-2 |Congruent triangles |45-47 |
|7-5 |SsA condition and HL congruence |47-48 |
|7-6 |Tessellations |49-50 |
|7-7 |Properties of parallelograms |50 |
|7-7P |Bouncing off the walls |51 |
|7-9 |Exterior angles |52 |
| | | |
|8-1 |Perimeter of a regular polygon |53 |
|8-2 |Area of a rectangle |53-54 |
|8-2P |Optimal quadrilaterals |54-55 |
|8-3 |Areas of irregular polygons |55-56 |
|8-4 |Area of a triangle |56-58 |
|8-4P |Triangle in a rectangle |58-59 |
|8-5 |Area of trapezoids |59-61 |
|8-6 |Pythagorean Theorem |61-62 |
|8-7 |Circumference and arc length |62-63 |
|8-8 |Area of a circle through data analysis |64-66 |
|8-8P |Area of tangent circles |66-67 |
| | | |
|9-5 |Famous paths in geometry............................................... |68-69 |
| | | |
|10-6 |Creating a toolbar to reference formulas |70-71 |
| | | |
|11-6 |Distance formula |72-73 |
|11-7 |Equations of circles |73-75 |
|11-8 |Means and midpoints |75-76 |
|11-8P |Midpoints and areas |77-78 |
| | | |
|12-1 |The transformation sk |78-79 |
|12-2 |Size changes |80 |
|12-3 |Properties of size changes |81 |
|12-4 |Proportions |82 |
|12-5 |Similarity |82-83 |
|12-6 |The fundamental theorem of similarity |84 |
| | | |
|13-1 |The SSS similarity theorem |84-85 |
|13-2 |The AA and SAS similarity theorems |85-86 |
|13-2P |Triangles in a trapezoid |86-87 |
|13-3 |The side splitting theorem |87 |
| | | |
| |Index |88-91 |
| |Variable Index |92-93 |
INTRODUCTION TO THE TI-92
Objective: In this activity, you will practice some of the basic functions of the geometry on the TI-92 calculator, including use of the Pointer, Point, Line, Measure, and Construct toolbars.
EXPLORATION 0-1. HEY, MY SCREEN ISN'T DARK ENOUGH (TOO LIGHT)!
Turn the calculator . and will darken your screen one notch if necessary. and will lighten your screen one notch if necessary. Repeat until you reach the desired contrast. And once you’ve gotten your screen adjusted the way you like it, you can reduce glare by snapping the lid to the calculator. You may find it easier not to do this, however, and that’s fine, too.
EXPLORATION 0-2. OOPS! I PRESSED THE WRONG KEY
There are a lot of keys in this small hand-held computer (large calculator). Therefore, it is natural to press the wrong key at the worst possible moment (that's called Murphy's Law). When you press the wrong key, press the button to get you back to where you started. Also, press when you want to return to the pointer (cross). Get in the habit of pressing the escape key when you’re done with a certain feature.
EXPLORATION 0-3. CREATE A NEW FOLDER
First, you need to create a folder to save all of the work you do in this course.
Press , and 5:Create Folder. Type your name in the Folder: box and press twice. A folder with your name should now appear in the directory. You should not need to do this again for the remainder of the year.
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EXPLORATION 0-4. CREATE A NEW GEOMETRY DOCUMENT
Start the geometry program by pressing , and choose 8:Geometry » 3:New... to begin. When you select Geometry and New you can either press the corresponding number (8 and then 3) or you can arrow down using the arrow pad (blue wheel). Use the arrow pad to arrow right and arrow down to your name and press to change the Folder: to your name. Arrow down (do not press enter) and type points in the Variable: box and press twice. You should now see a pointer (cross) at the center of the screen and a bunch of tools to represent menus at the top. Use this process each time you want to create a new geometry file. You may have to refer back to this page until you get comfortable with it.
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Now take a minute to explore the different function keys, or F-keys, like F1, F2, . . . Don’t actually select any particular function. Just select each function key and see what options are in that menu.
EXPLORATION 0-5. CREATE, LABEL, AND MOVE POINTS.
Press and choose 1:Point. Note the cross has changed to a pencil, meaning that you are ready to create points on the screen. Use the arrow pad to move the pencil to any location on the screen and press . Immediately type A to name the point. To make capital letters (which is customary for points) just hit
It is best to immediately type the letter before another point is created. If you keep creating points, it’s much more difficult to label the points. Use the arrow pad to move the pencil away from the point so you can see it on the screen. Press again to make another point and immediately type B to name it. Repeat this process until you have made five points named A through E.
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If you forget to label or mislabeled a point, first press to get out of the point making function. Your calculator can’t read your find and will assume you’re making more points until you tell it otherwise. After hitting you should see the pointer (cross), move the arrow pad over to the point until the screen reads THIS POINT, press and choose 4:Label, press , use the left arrow key (2 keys to right of space bar) to delete the old label (if there was one), type in or replace the label, and press .
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Press if the pointer (cross) is not on the screen. Use the arrow pad and move on top of point c until the screen reads THIS POINT. Hold down the with your left thumb and move point c around the screen by using the arrow pad with your right thumb.
Note: The and arrow pad (blue wheel) together function like a mouse. Just like when you click and drag something on the computer with a mouse you must hold the button down, on the TI-92 you must hold the
button down while you use the arrow pad for the movement.
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|Now let's just reposition (or drag) the label. Use the arrow pad and | |
|move on top of the label for point c until the screen reads THIS LABEL. | |
|Hold down the with your left thumb and move the label for point c with | |
|the arrow pad . | |
| | |
|Move the points and labels around until your screen matches the one shown| |
|to the right. When you move a point the label follows. | |
EXPLORATION 0-6. CLEAR SCREEN/DRAW SEGMENT/CORRECT AN ERROR
Let's start over with a fresh screen by pressing and choosing 8: Clear All. The calculator will ask you to press enter to confirm this request.
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|Next draw a segment anywhere on the screen by pressingand 5: Segment. | |
|Notice that the icon in the "toolbar" across the top of the screen for F2| |
|has changed from a point to a segment. Use the arrow pad to move to | |
|where you want the segment to start, press -- don't forget to type a | |
|letter immediately after so you don't have to use the label command. | |
|Then repeat for the other endpoint and type a label. | |
The following information is needed when you make an error. If you press the wrong key, press to clear the command. Let's practice deleting things. First press to get back to the pointer and to tell the calculator that you're no longer interested in making segments. Move the key pad on top of the object until it says THIS SEGMENT (it won't say this if you point at the endpoints -- you need to move inbetween the points somewhere), press , press and choose 7:Delete (or press the LEFT ARROW). Notice that the points are still on the screen. You could delete each separately, but instead select a point and then hold down the shift key (the UP ARROW).
EXPLORATION 0-7. CREATE TWO INTERSECTING LINES
CREATE A NEW DOCUMENT (even though your screen is blank -- you need to practice) with the variable lines. Refer to Step 4 if you forgot. Get in the habit of 1. referring back when you forget something, then 2. ask a group member, then 3. ask the teacher if needed and I'll be glad to help.
A line can be created with two points. Select and choose 4:Line. Move the pencil to the lower-right side of the screen and press . Label this point A. Move the pencil to the upper-left side of the screen so that the line is on a diagonal and press . A line like this, which is neither horizontal nor vertical, is called oblique. Create another line so that the two lines create a large X as shown to the lower-left. Label the point on the second line B.
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Press and choose 3:Intersection Point. Move the pencil to the intersection point until the message POINT AT THIS INTERSECTION appears. Press , label this point C, and to return to the pointer. Move the cross to the upper-right hand portion of the screen until the screen reads THIS LINE. Press and choose 2:Point on Object, press , label this new point D (be careful not to label the line), then . Your screen should match the picture shown above to the right.
EXPLORATION 0-8. CREATE, MEASURE, AND CHANGE A CIRCLE
CREATE A NEW DOCUMENT with the variable circ.
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|A circle is formed by selecting a center and a point on the circle. The | |
|radius is the distance from the center of the circle to any point on the | |
|circle. Press and choose 1:Circle, press to mark the circle's center and| |
|type C for center, and move the pencil outward to establish the size of | |
|the circle's radius. Make a circle large enough to cover one-fourth of | |
|the screen and press to finish the circle. | |
Construct a radius by pressing & choosing 5:Segment, move the pencil on the circle's center, pressand then drag the segment to a point on the circle until the screen reads ON THIS CIRCLE, and press and type A. Press to return to the pointer.
Measure the radius of the circle by pressing and choosing 1:Distance & Length, move the pencil to the middle of the segment until the screen reads LENGTH OF THIS SEGMENT, and press . Press to return to the pointer, move the pencil on top of the radius measurement, press to select (dotted), and to delete the measurement.
Another method to measure the length of a segment is to find the distance between the endpoints by moving the pencil to one endpoint, pressing , moving to the other endpoint, and pressing . Press to return to the pointer, drag the measurement to the upper right-hand portion of the screen, press and choose 5:Comment, drag the pencil to the left of the measurement, press , type radius= , hit , and then drag the comment as needed. Consult the diagram below.
The circumference of the circle is the length around the circle. Measure the circumference by pressing and choosing 1:Distance & Length, move the pencil to the circle until the screen reads CIRCUMFERENCE OF THIS CIRCLE, and press . Type a comment (abbreviate with circum if you wish) for the measurement and drag it underneath the radius measurement .
The area of the circle is the amount of space inside the circle. Measure the area of the circle by pressing and choosing 2:Area, move the pencil to the circle until the screen reads THIS CIRCLE, and press . Comment (area=) and drag this measurement underneath the other measurements. Drag the circle to the left-hand side of the screen by moving its center as shown below to the left.
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You can change the size of the circle by moving the pointer on top of the circle, pressing , and dragging with the toward or away from the circle's center. Modify the measurements on your screen until they match the picture shown to the right above (within 0.1 cm and 0.3 cm2).
EXPLORATION 0-9. CREATE, MEASURE, AND CHANGE AN ANGLE
CREATE A NEW DOCUMENT with the variable angles.
An angle can be created with two rays. Press and choose 6:Ray. Move the pencil to the left-hand-center part of the screen and press . Label this vertex point B and direct the ray to the upper right-hand portion of the screen and press . Move the pencil on top of point B until the screen reads THIS POINT, press to make another ray, and direct the second ray to the lower right-hand portion of the screen and press . Create point A on the top ray and point C on the bottom ray by using and 2:Point on Object as shown in the diagram below to the left.
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Use the to move points A and C close to the vertex of the angle.
An angle can be measured if a point on one ray, the vertex, and a point on the other ray are selected. Press and choose 3:Angle. Move the pencil over point A and press , over point B and press , over point C and press . The measure of ................
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