Online Activity Sheet


Theorem: A triangle is a right triangle if and only if the median to the longest side

              (hypotenuse) is exactly half the length of this side.

Interactivity

  • Click and drag the slider a to change the length of the side \overline{AC}
  • Click and drag the slider c2 to change the length of the median (and the hypotenuse \overline{AB} ).
  • Click and drag the point C to move and the point A to rotate.
  • Click the checkbox to show triangle ABC.
Notice that \angle ACB appears to be 90^\circ .
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Questions to think about?

  • Deselect checkbox to hide triangle ABC
  1. What is: \alpha + \beta ?
  2. What kind of triangle is \triangle CAC'
  3. Why does \delta =\frac{\alpha}{2} ?
  • Select checkbox to show triangle ABC
  1. What kind of triangle is \triangle CBC'
  2. Why does \frac{\alpha}{2}+ \gamma = 90^\circ ?
Why does \angle ACB = 90^\circ
What part of the theorem have we shown?
Interactivity: Do the construction!

1. Look at the construction in the window above and then create this construction in the window below.

Help

  • Click on , then on point C and then type in "a" (letter a - no quotes) and hit Enter.
  • Click on , then on point C and type in "c2".
  • Do the same for point A.
  • or complete directions.
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Page last modified on January 28, 2009, at 12:43 PM