Bases and Heights of Triangles

Warmup

Draw one triangle with an area of 12 square units. Try to draw a non-right triangle.

Explain how you know the area of your triangle is 12 square units.


Activity #1

Construct  the Height that Corresponds to the Given Base of an Acute Triangle.

In the following activity, you are going to construct the height of a triangle when the base is given. We shall look at Acute triangles only.

Always remember to click on after every step before moving to the next step.

  • Click on ​the Bisector tool .
  • Click on the point A to select it.  ​
  • Click on BC. (A perpendicular line is constructed on BC through A.) ​
  • Click on  and click on the point where the constructed line and BC intersect, G. ​
  • To show that the line is perpendicular to BC, click on   and click on A, G, and B in that order.
  • AG is the height of the triangle for the given base.

Activity #2

Construct the Height That Corresponds to the Given Base of an Obtuse Triangle. 

In the activity below, you are going to construct the height of a triangle when the base is given. We shall look at Obtuse triangles only.

As usual, remember to click on after every step before moving to the next step.

  • ​Click on ​ the line tool .
  • Click on BC to construct a line through both points.​
  • Click on , and click on A. ​
  • Click on BC to construct a perpendicular line to BC.  ​
  • Click on the point tool   and click on the point of intersection of the two lines, D. ​
  • To show that the lines are perpendicular, click on   and click on B, D, and A in that order.
  • AD is the height of the triangle for the given base.


Activity #3

Construct the Height That Corresponds to the Given Base of a Triangle. 

In the following activity, you are going to construct the height of a triangle when the base is given. In the three applets, are copies of the same triangle. Each triangle is rotated so that the side chosen as the base is at the bottom and is horizontal.

  • Draw a height that corresponds to each base below.
  • Draw a line segment to show the height for the chosen base in each triangle.

Be sure to navigate through all the slides below.


Challenge #1

Be sure to navigate through all the slides below.


Challenge #2

For each triangle, a base is labeled b. Use the segment tool to draw a line segment that shows its corresponding height.


Challenge #3

Select all triangles that have an area of 8 square units.