Triangles - Medians and Right-Angle Triangles

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 .

• 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. This browser does not have a Java Plug-in. Get the latest Java Plug-in here.

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