Power with AnglesN                                                                                             

Name__________________

 

 

 

This exploration will allow us to gather data to explore relationships of chords, secant segments, tangent segments,

and the angles and arcs that they create. These relations are actually theorems in your book. When you are finished

with this activity, I encourage you…wait…you need to look in your book and see how this activity so nicely connects to

section 10.8 in your textbook. 

 

WORDS TO THE WISE… refer to these before you ask me questions.

1.  Measure ARC ANGLES (what we call arc measure), not arc lengths for this exploration.

            To measure the arc, you must construct the arc. So, select the center, then select the two points on the circle

in a counterclockwise order. Then “construct” the arc. Next, “measure” the arc angle.

2. To add an entry, your “tabulate” table (redundant?) must be highlighted.

3.  Put your name on anything you intend to print.  (hint: use a textbox) ONLY PRINT WHAT YOU NEED TO PRINT.

            You should have three sketches. If I see extra papers with your name on it, this will result in point reduction.

(Make sure your sketch is small enough to fit on one sheet of paper.)             

 

Exploration #1

                        1.  Construct and label circle O and the secants like the diagram to the left.

                        2.  Measure all of the following in order.

                                    -                - mÐAXB           - mÐAXC

                                    -                - mÐCXD           - mÐBXD          

                                    -                - mAB (arc)       - mAC (arc)

                                    -                - mCD (arc)       - mBD (arc)      

                        ORIENT THE MEASUREMENTS ON YOUR PAGE IN ONE VERTICAL COLUMN.

 

3.   Now select all of the measurements in order.

4.  Go to the Graph command on the command bar.  Select tabulate.  A list of

measurements and their values should appear in a table-like format. 

5  Highlight the “tabulate” table by clicking on any entry.  Go again to the

Graph menu and select “add table data”.

            6. Now change you picture by dragging any part.

7.  Repeat steps 5 and 6 at least 2 more times.  (There should be at least 4 measurements in your table.)

Use a text box to type your name above your sketch. Save sketch as Explor1 on your disk or in your

folder on the H: drive in a folder with your name on it.  Print your sketch.  Close the sketch. 

 

Exploration #2

Open a new sketch.

 

1.   Construct a diagram like the one to the left. Again, notice AD and BC

are secants that intersect at point X.

2.   Measure all of the following.

                       

- - --- mAB – mCD - ÐAXB                

 

ORIENT THESE IN ORDER VERTICALLY ALSO.             

3.Repeat directions 4-7 from above. 

 

 

Use a text box to type your name above your sketch. Save sketch as Explor2 on your disk or in your

folder on the H: drive in a folder with your name on it.  Print your sketch.  Close the sketch. 

 

 

Exploration #3

Open a new sketch.

                                                            1.   Construct a diagram like the one to the left. In this diagram, AX is a tangent line of circle O,

and BC is a secant that intersect the tangent at the exterior point X.

                                                                        To construct a tangent line, remember that a tangent line is perpendicular to the

radius of the circle.

                                                           

2.  Measure all of the following.

        -    -  - - ÐAXB – mAB – mAC

            ORIENT THESE IN ORDER VERTICALLY ALSO.  

               

3.  Now repeat directions 4-7 from exploration #1.      

 

Use a text box to type your name above your sketch. Save sketch as Explor3 on your disk

or in your folder on the H: drive in a folder with your

name on it.  Print your sketch.  Close the sketch.