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 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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