In or Out



In or Out?

Each triangle has three altitudes. The diagram above illustrates three red altitudes of a particular triangle. Given any triangle, do the altitudes lie on a side, on the inside, or on the outside of the triangle? How do your results depend on different types of triangles?

Using GSP, construct an acute triangle.  Find the altitudes of each side using the line choice.  Make the lines a light color and dotted.  Next, construct segments between each angle and opposite side.  Make these segments thick and a different color.  Label each angle and measure it.  Now, grab an angle and form various types of triangles.  When the triangle has a right angle, two of the altitudes lie on top of the sides forming the right angle.  When the right angle becomes obtuse (greater than 90 degrees), the altitudes going through the other angles, fall outside the triangle.  When the triangle is acute, the altitude falls inside the triangle.


Click here to view a triangle that shows this.