Triangles

In this lab, we'll be exploring a cool property of acute, obtuse, and right triangles that will lead us to one of the most famous theorems in the history of mathematics.
First, take a look at the graphic and notice the data labeled on the left. Notice the three points that make up a triangle in the middle of the three squares (A, B, and C). Click on point C and move it up and down the y-axis. What changes in the data on the left? Can you tell what the segments are representing? (Notice that when you click on one of the segments, something gets highlighted on the graph). Click and drag point A to move it around. What data changes on the left? Can you tell what the Polygon information is representing? Now you'll be filling out the chart that is shared with you on your Google Drive called "Square Triangles Template". First, make a copy of the chart so that you can edit it (this will save it to your Drive so that you can access it later). Move points A and C around so that you create an acute triangle. Using the data on the left, fill in the columns on the chart (leaving the blank column blank). MAKE SURE TO RECORD ALL OF THE DATA BEFORE YOU CHANGE YOUR TRIANGLE! Create three total acute triangles and record the data. (Remember - an acute triangle's biggest angle is less than 90 degrees) Next you'll create some right triangles. To do this, move the points A and C onto whole numbers on the x and y axes. Record the data in your chart. In total, you should create four different right triangles. MAKE SURE TO RECORD ALL OF THE DATA BEFORE YOU CHANGE YOUR TRIANGLE! Finally, move points A and C to create three obtuse triangles, recording the information in your chart. (Remember, an obtuse triangle's biggest angle is greater than 90 degrees) MAKE SURE TO RECORD ALL OF THE DATA BEFORE YOU CHANGE YOUR TRIANGLE! When you are done filling in your chart, answer the questions below it on the Google Doc.