GEOMETRY. TI-Nspire Help and Hints. 1 Open a Graphs and Geometry page. (Press c 2 ).

Transcription

1 GEOMETRY TI-Nspire Help and Hints 1 Open a Graphs and Geometry page. (Press c 2 ). 2 You may need to save a current document you have been working on. Save or press e to move the cursor to No and press. 3 We do not need the axes. Turn off the axes or press b, View, Plane Geometry View. 4 You are ready to investigate geometry. Ensure your TI-Nspire is set to Degree measure. If not, press c, System Info, System Settings and set to Degrees. 5 Draw a line segment (Press b, Points & Lines, Segment). Move your cursor to a spot on the screen and press. Label your point A by pressing A (Press / g to have your points with capitals). Move your cursor to where you want the other end of the line segment to be and press. Name this point B. 6 If you move your cursor away from the line segment, you will see that you are still in line segment setting. We are investigating vertically opposite angles and angles on a line. Draw another line segment (and name the points). Press d to have the cursor as a pointer. 1

2 7 As we are going to measure angles, put an intersection point on the diagram where the line segments meet ( Press b, Points & Lines, Intersection Point(s) ). Placing the pointer near the intersection point, you will see that one of the line segments is bolded and the e icon is telling you that you can access other points/lines. Pressing e will show that you are at a point where the line segments meet. Press to tell the calculator that the line is selected and then press to select the second line. Name the point of intersection E. You will have a point of intersection inserted onto your diagram. 8 Press d to change to a pointer. Let s measure an angle ( AEC ). Press b, Measurement, Angle and move the cursor to Point A at the end of a line segment. Press and move your cursor to point E and press. Move to point C and press. The size of the angle is on the screen. Press d to change to a pointer. Move your cursor until it is over the angle measure. Press and hold the centre of the navpad until it locks (hand closes). Use your navpad to move the angle measure to where you want it to be and press. Press d to change to a pointer. 9 As you are in still measuring angle mode, measure the vertically opposite angle ( DEB ). Press d to change the cursor to a pointer. 10 Use your navpad to move the pointer to an end point of a line segment until the cursor changes to a hand. 2

3 11 Press and hold the centre of your navpad until the hand closes and locks. Use your navpad and move the point. Observe the changes in the size of the measured angles. 12 Press to release your point. Let s investigate the sum of adjacent angles on a straight line. Measure the size of an adjacent angle ( AED). Change to a pointer and place your cursor over the angle value, press the centre of the navpad to grab the angle and move it to where you want it to be and press d. 13 Press / g to change text to lower case. Press b, Actions, Text to insert a text box. 14 Move your pointer to a space well clear of the diagram and press. Insert a + b by using your keypad and press. Press d to change to a pointer. 15 We need to add calculations to our text box. Press b, Actions, Calculate. 16 Move your pointer to the text box and press. 3

4 17 Move your pointer to a measured angle. The value will flash. Press. The value will flash. 18 Move your pointer to the adjacent angle value and press. Move your calculated value near to the text and press. Press d to change your cursor to a pointer. 19 Move your pointer to the point at the end of the line segment and when the pointer changes to a hand, press and hold the middle of your navpad to lock the hand. Move the point around the screen. The measured angle values change, but the sum of the adjacent angles still sum to Investigate the sum of the angles of a triangle. Hide axes. Open a new Graphs and Geometry page. Press b, Shapes, Triangle (or use the Polygon) to draw a triangle. 21 Move your cursor to where you want the vertices of the triangle and press. Do not forget to label the vertices. 22 Measure the size of each of the internal angles (instruction 8). 4

5 22 As we are investigating the sum of the internal angles of a triangle, the text box will be a + b + c. 23 Sum the internal angles by following the same procedure as instructions 15 to 18. Move one of your vertices and observe the changes in the value of your measured angles. The use of the TI-Nspire can be extended to other geometry rules and proofs (for example, sum of angles of a quadrilateral draw a quadrilateral via the shapes and polygon commands). As seen in the above screen captures, the Construction and Transformation menus contain many commands and instructions to investigate geometry. 5