The following is NOT HOMEWORK unless you miss part or all of the class. See the Main Class Web Page for ALL homework and due dates.

1) Brad Findell's Elliptic/Spherical Toolkit for Sketchpad

2) Walter Fendt's Java Applet

and continuing with the other probelms as time allows.

1) Brad Findell's Elliptic/Spherical Toolkit for Sketchpad

2) Walter Fendt's Java Applet

Image of Sum of Angles

Image of Hyperbolic Pythagorean Thm Image

-Folding an angle bisector

-Folding the perpendicular bisector of a line segment

-Folding the perpendicular from a given point to a given line

-Folding the perpendicular through a point on a line

-Folding a line parallel to a given line through a given point

-Folding to show that the sum of the angles in a triangle is 180 degrees

-Folding the intersection of the altitutes of a triangle

-Folding the intersection of the angle bisectors of a triangle

-Folding the intersection of the perpendicular bisectors of the sides of a triangle

-Folding the intersection of the medians of a triangle

-Folding to show that the square on the hypotenuse is equal to the sum of the squares on the two other legs of a right triangle

-Folding to show that (x+y)(x-y)=x

Then go to the computer lab or library to work on finding book and web references for the Geometry of our Universe project.

Part 1: Similar Triangles - AA Similarity activity sheet from Exploring Geometry with Sketchpad. Leave the Explore More part until later.

Part 2: Use the Triangle_Similarity.gsp file (control click and save the file. Then open it from Sketchpad) to complete the Similar Triangles - SSS, SAS, SSA worksheet. Leave the Explore More part until later.

Part 3: Then complete the Similar Polygons Sketchpad activity sheet.

Part 4: Go back to the Explore More parts of the worksheets.

Create a segment with the ruler tool.

Using the arrowhead tool, choose one of the endpoints and the segment too (by holding down the shift key as you select them)

Under Construct, use the Sketchpad feature to construct a perpendicular line through the endpoint.

Use the point tool to choose a new point on the perpendicular.

Use the ruler tool to construct the segment between the 2 points on the perpendicular line (ie before you do this, the entire line has been created, but the segment does not exist).

Use the arrowhead tool to select only the perpendicular line (but not the segment you just constructed)

Under Display, release on Hide Perpendicular Line.

Use the ruler tool to complete the third side of your right triangle.

Measure the right angle to verify that it is 90 degrees.

Measure the length of the three sides of the triangle.

Once you have all three lengths, under Calculate, click on the measurement of the base of the triangle in order to insert it into your calculation.

Continue in order to calculate the base*base + height * height - hypotenuse *hypotenuse

Move the points of your triangle around in order to try and verify (empirically) the Pythagorean Theorem.

Sketchpad has some built in explorations. Take out the Computer Directions Sheet and follow the directions to open the pre-made sketches that come with Sketchpad 4. Once you are in the Sketchpad folder, click on Samples, then on Sketches, then on Geometry and finally, open Pythagoras.gsp For future reference, I will write this as Desktop/205Math(yourcomputersnumber)/Applications(MacOS9)/Sketchpad/ Samples/Sketches/Geometry/Pythagoras.gsp

Go through Behold Pythagoras!, Puzzled Pythagoras, and then Shear Pythagoras. Click on Contents to get to the other Sketches.

Read through Euclid's Proof http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI47.html along with the appendix of Sibley to try and understand it.

We come back together and go through Euclid's Proof of the Pythagorean Theorem.