Assignments 3, 4

Geometer’s Sketchpad

Assignment #3 – Polly Gone Mad!

Welcome to GSP!

Skills: Make line segments, measure angles, calculate sums of angles, drag points and change shapes of polygons.

1. Select the straight-edge tool on the left column. Draw a line segment. Then draw a triangle.

2. Select the arrow tool (The arrow at the top of the left column).

3. Select and unselect points or edges by clicking on them. Click on any white space and unselect everything.

4. Now unselect everything. Then click on one vertex with the arrow tool. The vertex should be highlighted. Click and drag the vertex by holding down the mouse button. What happens?

5. Unselect everything. Select two vertices of your triangle only. Then click and drag one of the selected vertices. What happens?

6. Select all 3 vertices of the triangle. Click and drag one of the vertices. Explain what happens.

** Help your neighbor or get help from a neighbor!

1. To measure one of the angles in the triangle click on 3 vertices in order so that the middle vertex is where the angle is located. Carefully unselect all vertices.

2. Name each vertex by selecting the text and label button on the left column. The button has a capital A on it. Notice that the pointer is now a “We’re number one!” finger. Click on each vertex and name the vertices.

3. Select the arrow tool, and unselect all the vertices.

4. Now select all the vertices in a way so that the vertex labeled A is second.

5. Go to the MEASURE menu. Then select ANGLE. What is the result?

6. Continue to measure all three angles. Make sure you unselect everything every time you calculate something new.

7. To calculate the sum of all 3 angles go to the MEASURE menu. Select Calculate… You’ll see a calculator setup. Move your pointer over boxes on your sketchpad that has the measures of the angles of each vertex. They should all be lined up somewhere, usually at the top. Click on one of the angles. Then click on the + sign. (The measures of the angles should be highlighted.) Click on another angle and click on the + sign. Click on the last angle and THEN click on OK. What happens?

** Help your neighbor or get help from a neighbor!

Some definitions: A polygon is a closed curve with n sides. Each side must be a line segment (no curves). The term closed means that the polygon must not have an opening or gap. Another way to think of this is that the polygon must have an interior and exterior. A convex polygon is one with the following property: the line segment connecting any two interior points must lie completely in the interior of the polygon.

Poly Gone Mad!!

1.) What is the sum of the measures of the interior angles of a triangle?

2.) What is the sum of the measures of the interior angles of a convex quadrilateral? (A quadrilateral has 4 sides)

3.) What is the sum of the measures of the interior angles of a convex pentagon?

4.) What is the sum of the measures of the interior angles of a convex hexagon?

5.) What is the sum of the measures of the interior angles of a convex 7-gon?

6.) What is the sum of the measures of the interior angles of a convex n-gon, where n is greater than 7? Look for a pattern and find a formula.

7.) Give a specific example of a situation where you could use the formula to help you determine an unknown angle.

8.) Does the formula hold for non-convex polygons?

Assignment #4 – Properties of Lines and Parabolas

Open GSP

Properties of Lines

1. Go to the graph menu. Select SHOW GRID.

2. Go to the graph menu. Select NEW PARAMETER. Name the parameter “a” and set it to some value like 1. You can reset it later.

3. Go to the graph menu (yet again). Select PLOT NEW FUNCTION. Enter the function a*x. You can find the parameter “a” under the “values” tab.

4. Select many different values for the parameter “a” by double-clicking on “a” on the sketchpad. Write down what the parameter does, by typing in your results using a textbox. To create a textbox, click on the “A” on the left margin. Then double-click on a location where you want to type.

Properties of Parabolas

5. Save your sketch. Open a new sketch. Show the grid.

6. One of the standard forms of a parabola is y = a*(x-h)^2 + k. This form has 3 parameters, a, h, k. The carrot (^) is used for exponents. Create these three parameters.

7. Then plot a new function given by a*(x-h)^2 + k.

8. Play with each of the parameters a, h, k, and explore what each parameter does. Then write your results into a textbox.