Geometry Activity: Discovering Properties of Kites C.C. Edwards Casio Classpad 300 vs. TI-89 CALCULATORS: Casio: ClassPad 300 • Texas Instruments: TI-89, TI-89 Titanium Using the Casio ClassPad 300 Discovering Properties of Kites A kite is a quadrilateral having two pairs of distinct congruent sides, as illustrated in the figure at the right. It’s a square with one Vertex vertex moved away from its opposite vertex. Angles Major The longest diagonal of the kite is the major diagonal and the Diagonal other diagonal is the minor diagonal. The angles at the ends of the major diagonal are the vertex angles, and the other two angles are referred to as the non-vertex angles. In a square or rectangle, the diagonals are equal and bisect each other. In a square, they are perpendicular. What’s the relationship between the diagonals of a kite? In a parallelogram, the opposite angles are congruent. In a square, the diagonals bisect the vertex angles. What can be said about the angles of a kite? Here’s how to investigate these properties using a ClassPad 300. Start a geometry session: • Use the stylus to tap Menu on the Icon Panel. •Tap Geometry to start a geometry session. Start a new file: •Tap File on the Menu bar. Casio ClassPad 300 vs TI-891 © Casio, Inc. • For Classroom Use Only Using the Casio ClassPad 300 • Discovering Properties of Kites (continued) •Tap New in the drop down menu. •Tap OK to clear the screen and start a new file. Create a kite: •Tap the down arrow on the third drop down box. •Then tap the Kite tool. Kite Tool •Tap and drag the stylus to form a box, as pictured above. • Lift the stylus to create the kite, as pictured above. Create the diagonals of the kite: •Tap the down arrow on the second drop down box. •Then tap the Segment tool. Segment Tool •Tap point A, and then tap point C. •Tap point D, and then tap point B. Casio ClassPad 300 vs TI-892 © Casio, Inc. • For Classroom Use Only Using the Casio ClassPad 300 • Discovering Properties of Kites (continued) Construct the point of intersection of the diagonals: •Tap the Select tool on the label of the first drop Intersection down menu. Tool •Tap diagonal AC to select it. Then tap diagonal DB. •Tap the down arrow on the fourth drop down box. •Then tap the Intersection tool. Investigate the properties of the diagonals of the kite: •Tap the arrow at the right of the Toolbar. As illustrated in the first figure below, the angle between the diagonals is 90o. •Tap a blank area of the screen to deselect the diagonal. Then drag a vertex of the kite to change its shape, as illustrated in the second figure below. •Tap a blank area of the screen to deselect the vertex you just moved and then tap the diagonals to select them. As illustrated in the third figure below, the diagonals remain perpendicular. CONCLUSION: The diagonals of a kite are perpendicular. •Tap a blank area of the screen to deselect the diagonals. •Tap point D. Then tap point E, the point of intersection of the diagonals. Casio ClassPad 300 vs TI-893 © Casio, Inc. • For Classroom Use Only Using the Casio ClassPad 300 • Discovering Properties of Kites (continued) The length of segment DE appears in the measurement box, as illustrated in the figure at the right. Take note of this measurement. •Tap a blank area of the screen and then tap point B and then tap point E. The measurement appearing in the measurement box shows that DE = BE. CONCLUSION: The major diagonal of a kite bisects the minor diagonal. Investigate the properties of the angles of the kite: •Tap a blank area of the screen and then tap segments AD and DC to select them. The measure of angle ADC appears in the measurement box, as illustrated in the figure at the right. Take note of this measurement •Tap a blank area of the screen and then tap segments AB and BC. The measurement appearing in the measurement box shows that ЄADC = ЄABC. CONCLUSION: The non-vertex angles of a kite are congruent. This is not always the case for the vertex angles. •Tap a blank area of the screen and then tap segments AD and AC to select them. The measure of angle DAC appears in the measurement box, as illustrated in the figure at the right. Take note of this measurement. •Tap a blank area of the screen and then tap segments AB and AC. The measurement appearing in the measurement box shows that ЄDAC = ЄBAC. •Repeat this process to show that ЄDCA = ЄBCA. CONCLUSION: The major diagonal of a kite bisects the vertex angles. This is not always the case for the minor diagonal and the non-vertex angles of the kite. Casio ClassPad 300 vs TI-894 © Casio, Inc. • For Classroom Use Only Geometry Activity: Discovering Properties of Kites C.C. Edwards Casio Classpad 300 vs. TI-89 CALCULATORS: Casio: ClassPad 300 • Texas Instruments: TI-89, TI-89 Titanium Using Geometer’s Sketchpad on a TI-89 Titanium Discovering Properties of Kites Major disadvantages of using Sketchpad instead of the Classpad 300: • Unlike the Classpad 300, Sketchpad on a TI-89/92 Plus or Voyage 200 is not capable of constructing special shapes such as a kite. In fact, it isn’t even capable of constructing regular polygons. To construct a kite using Sketchpad you need to: 1. Construct the major diagonal. 2. Construct the two incongruent sides on the same side of the major diagonal. 3. Mark the major diagonal as a mirror. 4. Select the two sides. 5. Select the point of intersection of these sides. 6. Reflect the selected items in the major diagonal. • Activating the Segment tool in Sketchpad takes six keystrokes: ▲ ▲ 2nd F3 ▲ ENTER On the Classpad it takes at best two taps on the screen with the stylus. • Using the Arrow keys to move the cursor on the TI-89 screen is far more tedious than simply tapping the screen with the stylus as one does with a Classpad. The Casio Advantage... • Abiity to construct special steps like kites • Pen touch for easy manipulation • Large screen makes it easy to see •The ClassPad 300, unlike Sketchpad on a TI-89 or Voyage 200, has the ability to move and anchor a point on a line. Casio ClassPad 300 vs TI-895 © Casio, Inc. • For Classroom Use Only.