Open GSP
Sketch
Step 1 : Construct segment AB.
Step 2: Construct circles AB and BA by center (one at A, one at B) and radius (segment AB).
Step 3: Construct segment AC and segment CB, where C is one point of intersection of the circles.
Step 4: Construct D, the midpoint of segment AB.
Step 5: Constuct segments CD and DB.
Step 6: Hide the circles, point A, segments AB and AC.
Step 7: Relabel segments DB,DC, and CB as a,b, and c respectively. Relabel the vertices to correspond to the opposite sides.
Click here if you only have the demo version of GSP.
Investigate
Before you measure, can you guess the relationship between a and c ? Measure a,b, and c. Use Calculate to find c/a and b/a. Drag B to change the size of your triangle. Do the ratios c/a and b/a change? Do you recognize this number b/a when it's rounded to the hundreths place? Try multiplying it by itself.
In your Journal, write your conjectures.
Save this sketch as right3060.gsp to your computer.