Altitudes of a triangle. Orthocenter

[size=100]The applet shows the altitudes of triangle ABC as [math]h_a[/math], [math]h_b[/math] and [math]h_c[/math].[/size]

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1. Altitude of a triangle is:

perpendicular line that divides a side of a triangle in half the lenght connecting the vertex of a triangle to the midpoint of the opposite side perpendicular line from the vertex of a triangle to the opposite side

2. Does the position of the orthocenter affect the type of triangle ? [br] If you are not sure about the answer, change the position of the triangle's vertex in the applet above.

no yes

3. If the orthocenter is outside the triangle, what type of triangle is it ?

equilateral triangle abtuse triangle acute-angled triangle right triangle

4. What is the position of the orthocenter in a right triangle ?

outside of the triangle in the right angle of the triangle inside of the triangle

5. What is the relationship between the lenght of the side and the corresponding lenght of the altitude ?

These are proportional sizes. They are inversely proportional sizes.

6. If the sizes of the triangle are 5cm, 11cm and 12cm, the shortest altitude is:[br][br]Use Heron's formula to calculate the area of the triangle.

[math]\frac{12\sqrt{21}}{11}cm^2[/math] [math]\frac{12\sqrt{21}}{5}cm^2[/math] [math]\sqrt{21}cm^2[/math]

Altitudes of a triangle. Orthocenter

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Information: Altitudes of a triangle. Orthocenter