Open GSP and
Sketch
Step 1: Construct circle AB and segment AB.
Step 2: Construct a line perpendicular to segment AB through A.
Step 3: Construct segment AC where C is the intersection of the circle and line. Hide the circle and line.
Step 4: Construct BC.
Step 5 Measure AC,AB, and CB.
Click here if you only have the demo version of gsp.
Investigate
AC and AB,of course, should be equal. Can you guess what the measures of angles ACB and ABC are without measuring them? Measure them to confirm your conjecture. Now,there's a special relationship between the length of the hhypotenuse in an isosceles right triangle and the length of one leg. Use Calculate to the the ratio CB/AB. Do you recognize this number? If not try multiplying it by itself in Calculate . Manipulate your triabgle to make it bigger or smaller. Does CB/AB chhange? What is this ratio?
In your Journal, write your conjectures.
Save this sketch as isoright.gsp to your computer.