Name______Date______Period______Geo w/ Trig H.

Sketchpad Basics:

  • The tools are located on the left side of the window. The first 4 tools are used to select or draw figures: select ,

point , circle , segment/ray/line (click and hold for each option .)

  • When a new figure is drawn or added to the screen, it will be highlighted. Sketchpad keeps multiple items highlighted at the same time. To deselect an item, click it. To deselect all the items, click on blank space.
  • Sometimes Sketchpad will automatically name new points as they are drawn. If you want to change the name, or a point has not been automatically named, use the text tool , and double-click on the point. This opens a menu where you can enter a name.

Setup: Use the line tool to draw a line and then label its two points as A and B. Use the point tool to draw a point below the line and then label it point C.

Construct: Use the selection tool to select the line and the point. In the Construct menu, choose Parallel Line. Draw another point on this new line (to the right of C) and label it point D. Deselect everything. Drag either point A or B to move the first line around. Note that the lines remain parallel.

Explore: Draw a transversal for these two lines that intersects them at two new points (the transversal should pass in between pointsA and B and points C and D.) Use the point tool to draw the points of intersection (hover over the lines with the point tool until both are highlighted, then click) and label them E and F. Then, create points G and H on the transversal, above and below the parallel lines, respectively.

  1. Measure each of the eight angles. To measure an angle, select all three points in order (so the vertex is the middle one,) and go to the Measure menu. Choose Angle. Drag the measurements so they are inside the angles.
  1. Look at the measures of the special angle pairs (corresponding, alternate interior, alternate exterior, and consecutive interior). Mentally form some conjectures about the relationship between the special angle pairs.
  1. Are your conjectures always true? Move the three lines around by dragging any of the points on the lines and check to see if your conjectures remain true, even when you move the lines. Can you make them not be true?

Conclude: Use your observations to fill in the theorems below. Mark the diagram to represent the theorem.

If two ______lines are cut by a ______, then the ______are ______.
/ If two ______lines are cut by a ______, then the ______are ______.

If two ______lines are cut by a ______, then the ______are ______.
/ If two ______lines are cut by a ______, then the ______are ______.

Extension: Do the lines need to be parallel in order for linear pairs to be supplementary? ______

Do the lines need to be parallel in order for vertical angles to be congruent? ______

Setup: Start a new sketch. In the File menu, choose New sketch. Use the line tool to draw two lines. Do not make them appear parallel, but do not make them intersect on screen. Name the points on the first line R and S, and the points on the second line T and U.

Construct: Draw a transversal for these two lines. (Make sure your transversal passes in between R and S and T and U.) Create the points of intersection and name them V and W. Then, create points X and Y on the transversal, above and below the two lines, respectively.

Explore:

  1. MeasureRVW and TWY. Drag the measurements so they are inside the angles. Note that these are corresponding angles. Drag point R until you make RVW and TWY as close to congruent as possible. What do you think happened to and as a result of making these corresponding angles congruent? Make a conjecture:
  1. Let’s verify your conjecture by finding the slopes of and Highlight and and in the Measure menu, choose Slope. Is your conjecture correct? Change the measuresRVW and TWYso that they are different than before, but still congruent to each other. Is your conjecture still correct?
  1. Move point Rso that the angles are no longer congruent. Delete the measures of RVW and TWY and the slopes of and from the screen. (The grid will stay.)
  1. MeasureSVW and UWV. Drag the measurements so they are inside the angles. Note that these are consecutive interior angles. In the Measure menu, choose Calculate. Click on the measure of SVW, then the plus sign on the calculator, and then the measure of UWV. The sum of the measures will appear on the screen. Drag point R so thatSVW and UWV are as close to supplementary as possible. What do you think happened to and as a result of making these consecutive interior angles supplementary? Make a conjecture:
  1. Let’s verify your conjecture by finding the slopes of and Is your conjecture correct? Change the measuresSVW and UWVso that they are different than before, but still supplementary to each other. Is your conjecture still correct?

Conclude:

  1. Use your observations to fill in the theorems below.

  • If two lines are cut by a transversal so that the ______are ______, then the lines are ______.
  • If two lines are cut by a transversal so that the ______are ______, then the lines are ______.
**There are two more theorems just like these!**
  1. How are these new theorems related to the theorems on the front?