Sketch
The sketch below shows a right triangle with squares constructed on its three sides. You can drag vertex A to change the size and shape, but it will remain a right triangle.
Applet 1 starten
Investigate
- Click "Construct Center of Square" to show center O of the square on the longer leg. The center of a square is located at the intersection of the diagonals.
- Click "Construct j and k" to show two lines through O: line j perpendicular to the hypotenuse and line k perpendicular to line j. Lines j and k divide the square on the longer leg into four quadrilaterals. Click "Construct Quadrilaterals" to show the quadrilaterals and the square on the shorter leg.
- Click "Hide Construction Lines." Now move the green quadrilaterals in the square on leg b into the square on the hypotenuse by dragging points P and P'.
- Move the yellow quadrilaterals in the square on leg b into the square on the hypotenuse by dragging points Q and Q'.
- Move the pink square in the square on leg a into the square on the hypotenuse by dragging point R.
- Formulate the Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. If a and b are the lengths of the legs, and c is the length of the hypotenuse, then _____.
Sketch
Use this sketch to investigate whether or not the Pythagorean Theorem works for all triangles. The triangle in the sketch is not a right triangle and you can drag any of the vertices to change the triangle. Click the button if you want to make it into a right triangle.
Applet 2 starten
Investigate
- When is a2 + b2 equal to c2?
- When is a2 + b2 greater than c2?
- When is a2 + b2 less than c2?