Geometry
Ratio of Areas
Name:
This exploration is divided into 3 activities. Each group member is responsible for the
TI-92 on one activity; all group members are responsible for developing a conjecture.
Be prepared to share group conjectures.
Activity 1
Construct 2 triangles that have the same height but different bases. Measure the
areas, the heights, and the bases. Find the ratio of the areas, the ratio of the heights,
and the ratio of the bases. Make a conjecture about the ratio of the areas.
b1
b2
h1
h2
A1
A2
b1/b2
h1/h2
A1/A2
Conjecture:
Activity 2
Construct 2 triangles that have the same base but different heights. Measure the
areas, the heights, and the bases. Find the ratio of the areas, the ratio of the heights,
and the ratio of the bases. Make a conjecture about the ratio of the areas.
b1
b2
h1
h2
A1
A2
b1/b2
h1/h2
A1/A2
Conjecture:
Activity 3
Construct 2 similar triangles that have different heights and different bases. Measure
the areas, the heights, and the bases. Find the ratio of the areas, the ratio of the
heights, and the ratio of the bases. Make a conjecture about the ratio of the areas.
b1
b2
Conjecture:
h1
h2
A1
A2
b1/b2
h1/h2
A1/A2