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 .
Questions to think about?
- Deselect checkbox to hide triangle ABC
- What is: \alpha + \beta ?
- What kind of triangle is \triangle CAC'
- Why does \delta =\frac{\alpha}{2} ?
- Select checkbox to show triangle ABC
- What kind of triangle is \triangle CBC'
- 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
|
, then on point C and then type in "a" (letter a - no quotes) and hit Enter.
, then on point C and type in "c2".
Related themes:
 Up one level
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