30-60-90

Right Triangle

Activity


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.

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