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### TI-83 Plus: Constructions with Cabri Jr.

Presented by Judy O’Neal, North Georgia College & State University ([email protected])

Cabri Jr. APP

F1

Undo

New

Open

Save as

Quit

F2

Point

Point

Point on

Point of Intersection

Line

Segment

F3

Perpendicular line

Parallel line

Perpendicular Bisector

Angle Bisector

Midpoint

F5

Alph-Num

Measure

Distance & Length

Angle

Slope

Clear

Moving/dragging

Calculator Skills AddressedMathematics Topics Addressed

- Basic geometric constructions
- bisecting a segment
- bisecting an angle
- constructing a perpendicular bisector of a line segment
- constructing a perpendicular from a point to a line
- constructing a line parallel to a given line through a point not on the line

Activating Cabri Jr.

- Press APPS.
- Arrow down to Cabri Jr (or press ALPHA C to move the cursor quickly to the C’s) and press ENTER.
- Press your favorite key.
- View one of the two screens at bottom right.
- If the F1 menus shows, press CLEAR to obtain a blank screen.

Drawing a Segment

- Press F2, arrow down to Segment, and press ENTER.
- A segment icon appears in the upper left-hand corner of the screen.
- Use the arrow keys to move the cursor (pencil) to the desired location for the first endpoint of the segment and press ENTER.
- A blinking point appears.
- Use the arrow keys to move the cursor to the desired location for the second endpoint and press ENTER.
- A dotted line segment appears as the arrow keys are used and a blinking point appears after pressing ENTER.
- Press CLEAR to exit the Segment tool.

Bisecting a Segment

- Press F3, down arrow to Midpoint, and press ENTER.
- The Midpoint tool appears in the upper left-hand corner of the screen.
- Use the arrow keys to move the cursor close to the segment so that it starts to “dance” (becomes moving dashes) and press ENTER.
- Press CLEAR to exit the Midpoint tool.

Verifying a Segment Bisector (Midpoint)

- Measure the distance between the midpoint and one of the endpoints.
- Press F5, down arrow to Measure, right arrow to D & Length, and press ENTER.
- Move cursor to one endpoint (it will blink) and press ENTER.
- Move cursor to the midpoint (it will blink) and press ENTER.
- Move the “hand” or “grab” tool using the arrow keys to desired location and press CLEAR.
- Repeat measuring distance between the other endpoint and the midpoint.
- Compare the distances.
- Press CLEAR to exit the Measure tool.

Labeling Points

- Press F5, arrow to Alph-Num, and press ENTER.
- Move cursor to one of the points (it will blink), press ENTER (a vertical bar appears), type a letter, and press ENTER.
- If the wrong letter is typed, immediately press CLEAR and retype the correct letter.
- Name the remaining points.
- Press CLEAR to exit the Alpha tool.

Moving Labels

- Move cursor to the label to be moved until a blinking underline and clear arrow appear and press ALPHA (grab tool appears).
- Use arrow keys to move the label to desired location and press CLEAR or ENTER.
- NOTE: Labels attached to points have a limited range of movement.

Saving and Clearing a Screen

- To save a screen,
- Press F1, arrow down to Save as, and press ENTER.
- Type a name for the file using the calculator keys (no need to access F5 Alph-Num) and press ENTER.
- To clear a screen,
- Press F5, arrow down to Clear, press right arrow, select All, and press ENTER.

Drawing an Angle

- Press F2, arrow down to Segment, and press ENTER.
- Draw a segment.
- NOTE: Cabri Jr. has no ray tool for constructing angles.
- Draw a second segment beginning at the end of the first segment, making certain that the point at the end of the first segment is blinking.
- Press CLEAR to exit the Segment tool.
- Label the angle.

Bisecting an Angle

- Press F3, arrow down to Angle Bisector, and press ENTER.
- Angle Bisector tool appears in upper left-hand corner of screen.
- Move cursor to select one of the non-vertex points (point will blink) and press ENTER (point will highlight).
- Move cursor to the vertex point and press ENTER when the point blinks.
- A dotted line will appear.
- Move cursor to the third point and press ENTER.
- The dotted will change to a solid line.
- Press CLEAR to exit the Angle Bisector tool.

Preparing to Measure Angles

- Press F2, choose Point, right arrow to Point on, and press ENTER.
- Move cursor to location of desired point (line will dance), press ENTER, and press CLEAR.
- Label new point.
- Press F5, select Alph-Num, press ENTER, move cursor, press ENTER, type label, press ENTER, and press CLEAR.

Measuring Angles

- To measure DEG
- Press F5, arrow down to Measure, right arrow to Angle, and press ENTER.
- Angle measure icon will appear in upper left-hand corner of screen.
- Move cursor to a non-vertex point D and press ENTER.
- Arrow to vertex point E (noticing that a dotted line appears) and press ENTER when the vertex point blinks.
- Move cursor to point G (dotted angle shows) and press ENTER.
- Move hand/grab tool, if desired, and press CLEAR.

Verifying Angle Bisection

- Measure GEF.
- Move cursor to a non-vertex point G and press ENTER.
- Arrow to vertex point E (noticing that a dotted line appears) and press ENTER when point E blinks.
- Move cursor to point F (dotted angle shows) and press ENTER.
- Move hand/grab tool, if desired, and press CLEAR.
- Observe the relationship of angles measures.
- If desired, measure FED to confirm total angle measure.

Moving a Point

- Move cursor to a non-vertex point and press ALPHA when point blinks and arrow becomes clear.
- Move point using the arrow keys to change angle measures.
- Press CLEAR to exit hand/grab tool.

Saving a Construction

- Press F1, arrow down to Save as, and press ENTER.
- Name the file ANGLEBIS and press ENTER.

Constructing a Perpendicular Bisector

- Open a NEW file.
- Press F1, arrow down to New, and press ENTER (a blank screen appears).
- Draw a segment.
- Press F2, arrow down to Segment, press ENTER, and press CLEAR.
- Construct the perpendicular bisector.
- Press F3, arrow down to Perp. Bis., and press ENTER.
- Arrow to the line segment (it will dance) and press ENTER.

Verifying Perpendicularity

- To measure the angle formed between the “supposed” perpendicular lines, construct a point at the intersection of the two lines.
- Press F2, select Point, arrow right and down to Intersection, and press ENTER.
- Notice the Intersection icon in the upper left-hand corner of the screen.
- Move cursor close to the intersection (both lines will dance), press ENTER, and press CLEAR.
- Press F2, select Point, arrow to Point on, and press ENTER.
- Move cursor to the top portion of the supposed perpendicular line and press ENTER.
- Move cursor to the bottom portion and press ENTER.
- Measure angles and drag to investigate.
- Angle measures do not move with the lines.

Drawing a Line

- Press F2, down arrow to Line, and press ENTER.
- Move the cursor to the desired location to begin drawing the line and press ENTER.
- Use the arrow keys to move the cursor to the desired location for the second point to anchor the line and press ENTER.
- A dotted line appears as the arrow keys are used.
- Press CLEAR to exit the Line tool.

Constructing a Perpendicular from a Point to a Line

- Draw a point not on the line.
- Press F2, select Point, right arrow to Point, and press ENTER.
- Notice the Point icon in the upper left-hand corner of the screen.
- Move cursor to desired location, press ENTER, and press CLEAR.
- Construct a perpendicular to the line through the point not on the line.
- Press F3, select Perp., and press ENTER.
- Notice the Perp icon in the upper left-hand corner of the screen.
- Arrow to the point, press ENTER, arrow to the line, press ENTER, and press CLEAR.

Investigating Distance

Task for Students:

- Explore how the distances from a point on the perpendicular bisector of a segment to each segment endpoint compare.
- Use F5, Measure, D & Length tool.
- Drag the point on the perpendicular bisector and observe what happens to the distances.
- Constructing segments (F2) may improve visualization.

Question for Students:

- What appears to be true about the distances from a perpendicular line to the endpoints of the line segment?

Undoing and Deleting

- To undo an action,
- Press F1, down arrow to Undo, right arrow to Undo, and press ENTER.
- The previous action is undone but there is no redo option.
- To delete an object,
- Press F5, arrow down to Clear, right arrow to Object, and press ENTER.
- Move cursor to object(s) to be deleted (they will dance) and press ENTER.
- Press CLEAR to exit the tool menu, if desired.

Constructing a Line Parallel to a Line Through a Given Point

- Using the previous line and a point not on the line,
- Press F3, arrow down to Parallel, and press ENTER.
- Move cursor to highlight the line and press ENTER.
- A blinking line will appear.
- Move the parallel line to the point not on the original line and press ENTER when the point blinks.
- Press CLEAR to exit the Parallel tool.
- Save drawing, if desired.

Verifying Lines are Parallel

- Use slopes to determine whether lines are parallel.
- Press F5, down arrow to Measure, right arrow to Slope, and press ENTER.
- Slope icon appears in upper left-hand corner.
- Move cursor to original line (it dances) and press ENTER.
- Move hand/grab tool to desired location and press CLEAR.
- Repeat process with parallel line.
- Press CLEAR to exit Slope tool.
- To drag original line,
- Move cursor to one of the points, press ALPHA, and arrow up or down.

Question for Students:

- What appears to be true about the slopes of parallel lines?

Quitting Cabri Jr.

- Press F1, arrow to Quit, and press ENTER.
- NOTE: The screen last displayed will reappear the next time Cabri Jr. is opened.

GPS Addressed

- M7G1
- Perform basic constructions using appropriate technology (bisecting a segment, bisecting an angle, constructing perpendicular lines including perpendicular bisector of a line segment, and constructing a line parallel to a given line through a point not on the line)
- M7P1
- Using appropriate technology, build new mathematical knowledge through problem solving

Websites for Additional Exploration

- Texas Instruments
- Latest operating system and Apps http://education.ti.com/educationportal/sites/US/nonProductMulti/apps_latest.html?bid=3
- Cabri Jr. Apps Resources – 45-Day Trial Kit Kithttp://education.ti.com/educationportal/sites/US/nonProductSingle/global_promo_geometry.html

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