People's Education Press Grade 8 Information Technology Volume 2 Geometry Experiment 1: Measurement and Calculation 1. Experimental purpose
1, learn some basic functions (measurement and calculation) in the measurement menu.
2. Master some basic measurement and calculation methods such as length, distance, perimeter, perimeter, angle, area and coordinates.
Second, the experimental environment
1. Geometer's Sketchpad software (version 4.07 or 5.00) is installed.
I have a mathematical formula.
Third, the experimental content
The bisector of a triangle is equal to the included angle between the two sides.
Fourth, the experimental steps:
1. Draw triangle ABC: Draw △ABC with line drawing tool and mark letters with marking tool.
2. drawing? The intersection of the bisector of BAC and the line segment BC D: Select point A, point B and point C (note that the vertex of the corner must be selected first), and click the menu command: Construct? Angular bisector, inches? Select status? Click the intersection of bisector and line segment BC with the mouse.
3. Hide the bisector: in the selected state, click the bisector with the mouse first, and then press the shortcut key? Ctrl +H？ (Equivalent menu command:? Show? Hide? )
4. Connect Point A and Point D: After selecting Point A and Point D, press the shortcut key? Ctrl+L？ (Equivalent menu command:? Structure? Line segment? )
5. measure? No, what else? CAD shows that these two angles are equal.
Experiment 2: Making similar triangles 1 with variable proportion. Experimental purpose
1, learn some specific functions of conversion in the tools menu.
2. News? Based on the center of the tag. Fixed ratio? Or press? Mark the scale? Zoom object
3. Can you press it? Fixed angle? And or press? The angle of the mark? Rotating object
Second, the experimental environment
1. Geometer's Sketchpad software (version 4.07 or 5.00) is installed.
I have a mathematical formula.
Third, the experimental content
1, and a ratio is marked by three points on the same line.
2. Let a triangle take one of its vertices as the center and scale it according to the scale of the mark.
3. Drag the ratio control point to make a chart? Answer? Xinghe? x？ Type conversion.
Fourth, the operation steps:
1, draw △ABC.
2. Draw a straight line and hide the two control points on the straight line.
3. Draw three points D, E and F on a straight line, and use the selection tool to select the three points D, E and F in turn. Transformation? - ? Mark the scale? , mark a ratio.
4. Select three sides and three vertices of the triangle and choose them from the menu? Transformation? - ? Zoom? Click point a after the zoom dialog box pops up, and confirm that the rotation center in the dialog box is a.
5. You can see the change of similar triangles by dragging point F to make a linear motion, and you can also help to understand it by measuring the related values.
Experiment 3: Folding a triangle into a polygon 1. Experimental purpose
1, master the motion between two moving points.
2, master the basic method of graphics movement on the path.
Second, the experimental environment
1. Geometer's Sketchpad software (version 4.07 or 5.00) is installed.
2. A device with a mathematical formula is installed.
Third, the experimental content
1. In order to facilitate observation, the dotted line segment between the symmetry center and each key point is connected, and the research object and the dotted line segment are rotated around the symmetry center by 1800 to form central symmetry.
2. Draw a corner and mark it.
3. Select the original object and the dotted line segment again and rotate according to the marked angle.
4. Drag the angle of the marker to 00, and the observed figure is centrosymmetric. Drag the angle of the marker from 00 to 1800, and rotate 1800 to see the overlapping process.
Fourth, the operation steps:
1, stand by.
2. Double-click the O point with the selection tool and mark it as the center.
3. At the same time, select points A, B and C, line segments AB, AC, BC, OA, OB and OC, and rotate around point O 1800.
4. Use the selection tool to ensure that these three points are selected in the order of D, E and F, and be careful not to select other objects. Transformation? - ? Mark corners? If the marking is successful, you will see a small animation.
5. Select points A, B and C and line segments AB, AC, BC, OA, OB and OC at the same time, and select from the menu? Transformation? - ? Spin? In the pop-up dialog box, make the settings as shown in Figure 5.
6. In order to facilitate observation, the objects rotated at all angles turn red.
7. Drag the point f to make the line segments EF and ED coincide, and you can see that the red triangle coincides with △ABC.
Note: In this example, the angle of the mark is a number. In this case, pay attention to the order of selecting three points and press? Points on the side, vertices, points on the side? If you want to choose, if you choose the counterclockwise direction, mark it as a positive angle; Clockwise, marking a negative angle will affect the rotation direction of the object.
The marked angle can also be the degree obtained by measuring the angle (which can only be a positive angle at this time) or the degree calculated by a calculator (which can be positive or negative).
Experiment 4: Quadratic Curve —— Construction of Ellipse, Parabola and Hyperbola 1. Experimental Purpose
1 to learn some basic functions of the menu.
2. Master the generation method of quadratic curve trajectory.
Second, the experimental environment
1. Geometer's Sketchpad software (version 4.07 or 5.00) is installed.
I have a mathematical formula.
Third, the experimental content
Using the properties of conic to construct conic (taking ellipse as an example)
Fourth, the experimental steps:
1. The drawing method of drawing circles and line segments is: in the state of drawing line segments, move the cursor into the circle, click once, release the left button, move the cursor to the circle, and click once to get the line segment CD.
2. The method of straight line AD between line segment CD and straight line AD is: in the straight line state, click point A, release the left button, move to point D and click.
3. Intersection point In the selected state, click the intersection point of two straight lines to get the intersection point E. ..
4. Build a trajectory. Select points E and D, and then click the menu command: Construction? Trajectory (u)
Hide unnecessary objects, select a circle, two straight lines and points e, d and b.
Try it: drag point C out of the circle and see what happens to the trajectory.
Experiment 5: Draw an isosceles triangle with symmetry transformation 1 Experimental purpose
1, learn some basic functions of transformation in the tools menu.
2. Will it be based on? The mirror image (symmetry axis) of the mark is symmetrical (taking isosceles triangle as an example)
Second, the experimental environment
1. Geometer's Sketchpad software (version 4.07 or 5.00) is installed.
I have a mathematical formula.
Third, the experimental content and steps:
1. Create a new geometry artboard file.
2. First, use tools to complete the drawing.
3. use? Choose tools? Double-click the line segment advertisement to mark it as a mirror image.
4. Make sure that only point B and line AB are selected. Menu? Transformation? - ? Reflection? .
5. Hide point D and line segment AD, and press Ctrl+H to hide these two objects.
6. Draw the third edge and change the label of the third vertex to C. ..
Drag one of the three vertices at will, and you can see that △ABC is always isosceles no matter how its shape changes.
Experiment 6: Making congruent triangles 1 by translation. Experimental purpose.
1, learn some basic functions of transformation in the tools menu.
2. Will it be based on? Mark vector, mark angle, mark distance? Making congruent graphics (taking congruent triangles as an example)
3. Master nine translation methods in rectangular coordinate system and four translation methods in polar coordinate system.
Second, the experimental environment
1. Geometer's Sketchpad software (version 4.07 or 5.00) is installed.
I have a mathematical formula.
Third, the experimental content and steps:
Four combination methods of polar coordinate transformation
Four methods can be combined in rectangular coordinate system.
There is a way to translate according to the vector of tags.
The drag point f moves on the line segment DE, which can demonstrate the coincidence and separation of two triangles and can be used to explain congruence.
Operating steps:
1, tie △ABC
2. Draw a line segment DE, and draw a small F on DE.
3. Use the selection tool to select point D, then point F, and select from the menu? Transformation? - ? Label vector? , marking the vector from point d to f.
4. Select three sides and three vertices of △ABC, and choose from the menu? Transformation? - ? Translation? In the pop-up dialog box, make the settings as shown in Figure 4 (if the vector is marked, it will be automatically set to translate according to the marked vector).
5. Mark the three vertices of the new triangle with the text tool.
Experiment 7: Making Symmetric Graphics by Mirror Reflection 1. Experimental Purpose
1, learn some basic functions of transformation in the tools menu.
2. Some plane graphics will be mirrored based on the symmetry axis.
Second, the experimental environment
1. Geometer's Sketchpad software (version 4.07 or 5.00) is installed.
I have a mathematical formula.
Third, the experimental content
From left to right, it is demonstrated that dragging the vertex of a triangle to change its position and shape can observe the dynamic symmetry relationship and related properties.
Fourth, the operation steps:
1. Draw a straight line with the line drawing tool.
2. Select this straight line from the menu? Transformation? - ? Mark the mirror? Mark this straight line as the axis of symmetry.
3. Draw a △ABC on the edge of the straight line.
4. Select all △ABC from the menu? Transformation? - ? Reflection? , and mark the vertices of the reflection triangle with the text tool.