Geometer s Sketch Pad Instructions Basic Constructions

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1 Geometer s Sketch Pad Instructions Basic Constructions Tool Menu Basic constructions will use the Selection Arrow Tool, Point Tool, Compass Tool, and Straightedge Tool. Familiarize yourself with the location of each tool in the tool menu. The Selection Tool will select multiple items. To use the tool, first click on the whitespace of the sketch. When the selection cursor changes from an angled cursor to a horizontal cursor, it is hovering over an object to be selected. Clicking the mouse over the item will select the item. Selected items have a red border. Construction #1 Midpoint of a Segment 1. Use the Straightedge Tool to construct a line segment. 2. Use the Selection Tool to select only the line segment. 3. From the Construct menu, choose Midpoint. 4. The midpoint will be placed on the segment. 5. Use the Text Tool to draw a text box on the document. Label the diagram Midpoint in the text box. If a menu item is not available, additional items may have been selected or the required objects have not been selected. Click the whitespace with the Selection Tool and re select the objects. Construction #2 Perpendicular to a line through a point not on the line. 1. Use the Straightedge Tool and Point Tool to construct a line segment and a point. 2. Use the Selection Tool to select both the segment and the point. 3. Choose Perpendicular Line from the Construct menu. 4. The perpendicular line will be constructed. 5. Use the Text Tool to draw a text box on the document. Label the diagram Perpendicular to a Line in the text box. Results of perpendicular to a segment through a point not on the line.

2 Construction #3 Perpendicular bisector of a line segment. 1. Construct a line segment. 2. Construct the midpoint of the line segment. (Repeat construction #1). 3. Construct the perpendicular line through the midpoint. (Repeat steps 2 4 of construction #2). 4. Use the Text Tool to draw a text box on the document. Label the diagram Perpendicular Bisector in the text box. Construction #4 Construct two congruent segments. There are a variety of methods. This is only one. (Can you come up with others?) We will use the compass tool to construct a segment of equal length. 1. Use the Straightedge Tool to construct a segment to be copied. 2. Construct a second segment longer than the first. 3. Use the Selection Tool to select the segment to be copied and one endpoint of the second segment. From the Construct menu, choose Circle By Center+Radius. 4. Find the intersection of the circle and the longer segment since the radius is equal to the segment radius to be copied. Use the Selection Tool to select the segment and the circle. From the Construct menu, choose Intersection. The point of intersection will be displayed. 5. To label points, use the Selection Tool to select only the four endpoints of the two congruent segments. Select the endpoints in the order you want the labels to be placed. From the Display menu, choose Show Labels. The points will be labeled in the order they were selected. In the drawing below, AB 6. If you wish to verify the length, select the endpoints of one segment at a time. From the Measure menu, choose Distance. The distance between the points will be displayed. CD. 7. Use the Text Tool to draw a text box on the document. Label the diagram Congruent Segment in the text box. Result of measurements of congruent segments.

3 Construction #5 Angle Bisector 1. Use the Straightedge Tool to construct an angle. 2. Select the angle to bisect using the Selection Tool. Click the whitespace and select three points with the middle point as the angle to be bisected. To bisect angle B in the image at the right, select the points A, B, and C or C, B, and A. B must be the middle point selected. 3. From the Construct menu, choose Angle Bisector and the ray bisecting the angle will be displayed. 4. Add a point to the ray by clicking the Point Tool on the bisecting ray. 4. To measure an angle, use the Selection Tool to A select three points defining the angle. Remember to click the whitespace to deselect all objects before selecting the angle. From the Measure menu, choose Angle. The measurement of the angle will D be displayed in the window. 5. Move the points of the angle by clicking and B dragging. The angle bisector and measurement of C each angle will be continuously updated. m ABD = Use the Text Tool to draw a text box on the document. Label the diagram Angle Bisector in m CBD = the text box. Save the file as Basic Constructions.gsp for your own use!

4 Geometer s Sketch Pad Concurrency Constructions Medians of a Triangle A median of a triangle is a segment from the vertex of a triangle to midpoint of the opposite side. Use Geometer s Sketchpad to determine what can be said about the three medians of the triangle? Acute Triangle Median 1. Construct an acute triangle using the Straightedge Tool. Snap the endpoints of each successive segment to the previous endpoints. (Diagrams will be labeled for reference. You are not required to label your diagrams. 2. Construct the midpoint of each side of the triangle (See Basic Construction #1). 3. Select each vertex and midpoint of the opposite side with the Selection Tool. From the Construct menu, choose Line to draw a line through the vertex and midpoint. (The median through B and F has already been drawn in the image above. Vertex A and Midpoint E have been selected.) 4. Construct each of the three medians. Select and drag the vertices of the triangle to observe the changes. What can be said about the medians of an acute triangle? Make a sketch of the diagram on your paper. 5. Use the Text Tool to draw a text box on the document. Enter the text Acute Triangle Median. 6. Save the file using your 3 initials and triangles similar to jlw_triangles.gsp without the quotes. Add a New Page Add a new page to the document by using the File Document Options menu. From the Add Page drop down box, add a Blank Page. Click on the OK button. A new page is created and a tab will appear in the bottom right corner of the window to switch between pages. Right Triangle Median Window Tab 1. Create a right triangle. Use the Straightedge Tool to construct a segment. Select the segment and one endpoint. Construct a perpendicular line through the endpoint. Select the perpendicular line. Use the Point Tool to create a point on the perpendicular line. Select the two remaining endpoints and use the Construct Segment menu to construct the hypotenuse of the right triangle.

5 2. Since the perpendicular is a line, you will have to create a segment to find the midpoint. Select the two points on the perpendicular line and choose Construct Segment. 3. Hide the perpendicular line. Click the whitespace to deselect all objects. Click on the perpendicular line but not on the segment. In the image at the right, click on the line in the region above the M or below the O. From the Display menu, choose Hide Perpendicular Line. The perpendicular line should now be hidden. 4. Find the midpoint of each side. Select the segment forming each side of the triangle and construct the midpoints. 5. Construct the medians. Select the vertex and midpoint of the opposite side, construct each of the three medians. 6. Use the Text Tool to draw a text box and label the document as Right Triangle Medians. 7. Select and drag the vertices of the triangle to observe the changes. Make a sketch of the right triangle medians on your paper and save the file again. Obtuse Triangle Median 1. Use the File Document Options to add another new page. Create an obtuse triangle and construct the medians. 2. Select and drag the vertices of the triangle. Observe the changes to the medians. 3. Use the Text Tool to draw a text box and label the document as Obtuse Triangle Medians. 3. Make a sketch of the obtuse triangle. Save the file. Altitudes of a Triangle An altitude of a triangle is the perpendicular segment from the vertex to the opposite side. Acute Triangle Altitude 1. Use the File Document Options to add another new page. Use the Straightedge Tool to create an acute triangle. 2. Construct the altitude from each vertex. Review Basic Construction #2 if you need assistance creating a perpendicular line. 3. Click and drag the vertices of the triangle. What can be said about the altitudes? Make a sketch of the altitudes. 4. Use the Text Tool to draw a text box and label the document as Acute Triangle Altitudes. Save the file. A B C Right Triangle Altitude 1. Use the File Document Options to add another new page. Construct a right triangle as described in the medians section. 2. Construct the altitude from each vertex. 3. Make a sketch of the diagram. What can be said about each altitude? 4. Use the Text Tool to draw a text box and label the document as Right Triangle Altitudes. Save the file.

6 Obtuse Triangle Altitude 1. Use the File Document Options to add another new page. Construct an obtuse triangle. 2. Construct the altitude from each vertex. 3. Make a sketch of the diagram. What can be said about each altitude? 4. Use the Text Tool to draw a text box and label the document as Obtuse Triangle Altitudes. Save the file. Perpendicular Bisectors of a Triangle The perpendicular bisector of the sides of a triangle is the perpendicular to the side passing through the midpoint of the side. Acute Triangle Perpendicular Bisector 1. Use the File Document Options to add another new page. Construct an acute triangle. 2. Construct the perpendicular bisector of each side. Refer to Basic Constructions #1 3 for help constructing the perpendicular bisector. 3. Move the vertices of triangle. What can be said about the perpendicular bisectors of each side of the triangle? 4. Use the Text Tool to draw a text box and label the document as Acute Triangle Perpendicular Bisectors. Save the file. A B C Right Triangle Perpendicular Bisector 1. Use the File Document Options to add another new page. Construct a right triangle. 2. Construct the perpendicular bisector of each side. 3. Move the vertices of triangle. What can be said about the perpendicular bisectors of each side of the triangle? 4. Use the Text Tool to draw a text box and label the document as Right Triangle Perpendicular Bisectors. Save the file. Obtuse Triangle Perpendicular Bisector 1. Use the File Document Options to add another new page. Construct an obtuse triangle. 2. Construct the perpendicular bisector of each side. 3. Move the vertices of triangle. What can be said about the perpendicular bisectors of each side of the triangle? 4. Use the Text Tool to draw a text box and label the document as Obtuse Triangle Perpendicular Bisectors. Save the file. Perpendicular Bisectors of a Triangle Construct the angle bisectors for each angle of the triangle. Continue the pattern of creating an acute, a right, and an obtuse triangle on a new page. Construct the angle bisector of each angle. Refer to Basic Constructions #5 for help constructing an angle bisector. What can you say about the angle bisectors in each triangle. Make a sketch of the triangle. Label each page. Save the file. Turning in your constructions! 1. Launch a web browser and go to 2. Login with your ID and password. 3. Using the Jump button, jump to my public folder. 4. Use the Browse button to select the sketchpad file with your constructions. Upload the file to my dropbox.

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