Ratios of areas of triangles
Compare areas without calculating them: triangles with a common height have areas in the ratio of their bases, a median halves a triangle, and a vertex moving on a parallel line keeps the area.
- Russia: grade 8
Guide
In the Russian programme this is Grade 8 geometry, chapter "Area": properties of area, the area of a triangle S = 12ah, the theorem on triangles with equal heights.
Main facts. Equal figures have equal areas; the area of a whole is the sum of the areas of its parts. If two triangles have a common height, their areas are in the ratio of their bases. If they have a common base and their vertices lie on a line parallel to it, the areas are equal.
The numbers under the figure are base times height, that is twice the area. Drag the coloured points and watch the numbers. Write solutions as Given, Find, Solution, Answer.
The "why" question asks for your own explanation; then compare it with the model.