Isosceles Triangle Investigation
Grade:
High School
Isosceles ΔABC is constructed so that AB = AC = 5. Use this tool to investigate the relationship between the area of the triangle and the length of its base (BC).
- Drag point C to change the base and height of isosceles ΔABC.
- The length of the base and the area of the triangle will be recalculated as the triangle is modified; additionally, a trace will be created by the movement of point L, which shows a graph of the area as a function of BC.
- Note that the triangle disappears if points B and C overlap (that is, if BC = 0). Similarly, the triangle will disappear if BC > 10, as this is a violation of the Triangle Inequality.
When does the area of triangle ABC reach its maximum? What is the relationship between the base and and height?
NCTM Standards and Expectations- Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.