Altitudes of Triangles

An altitude of a triangle is a segment drawn from a vertex perpendicular to the line containing the opposite side.

In this exercise we will be constructing the 3 altitudes of a triangle.

 

  1. Bring up a new sketch
  2. Under display choose line style thick
  3. Draw an acute triangle.
  4. Label the vertices A, B, and C
 

 


  1. Click in the blank part of your screen to make sure nothing is selected
  2. Under display choose line style dashed and color red. 
  3. On your tool buttons choose line instead of segment
  4. Choose points A and C and under the construct menu, line
  1. Choose points B and the line AC (dashed -red) and construct, perpendicular line.
  2. Choose the two dashed lines and construct , point at intersection. (label – point D)

 

 

 

 

 

 

 

 

  1.   Make sure that nothing is selected by clicking on the blank portion of your sketch
  2. Change your line tool on the left side back to segment, under display choose line thick.
  3. Using your arrow key, select points B and D and under construct choose segment.

We will repeat this process to construct the other two altitudes.

  1. Click on blank portion of your screen to make sure nothing is selected
  2. Under display choose line style dashed and color blue. 
  3. On your tool buttons choose line instead of segment
  4. Choose points A and B and under the construct menu, line

  1. Choose points C and the line AB (dashed -blue) and construct, perpendicular line.
  2. Choose the two dashed blue lines and construct, point at intersection. (label – point E)

  1. Make sure that nothing is selected by clicking on the blank portion of your sketch
  2. Change your line tool on the left side back to segment, under display choose line thick.
  3. Using your arrow key, select points C and E and under construct choose segment.

  1. Click on a blank portion of your screen to make sure nothing is selected.
  2. Under display choose line style dashed and color green. 
  3. On your tool buttons choose line instead of segment
  4. Choose points B and C and under the construct menu, line

  1. Choose points A and the line BC (dashed -green) and construct, perpendicular line.
  2. Choose the two dashed green lines and construct , point at intersection. (label – point F)
  3. Make sure that nothing is selected by clicking on the blank portion of your sketch

 


  1. Change your line tool on the left side back to segment, under display choose line thick.
  2. Using your arrow key, select points A and F and under construct choose segment
  1. Choose  the dotted line through BD and the dotted line through AF and under construct- Point of intersection.
  2. Label the point of  intersection and change the label to orthocenter.
  3. Use your text tool and write the definition of an altitude.

An altitude is a segment drawn from a vertex of a triangle perpendicular to the line containing the opposite side.