Make sure you are comfortable with the raw materials (congruent angles and proportional sides) before you try to build the similar triangles.

When you are ready, go back to the lab page.

1. Raw materials: construct congruent angles.
2. Raw materials: construct pairs of sides in proportion.
3. Use the AA (angle angle) theorem to build △DEF ~ △ABC. To do this, use your congruent angle raw material to construct ∠EDE' ≅ α and ∠DED' ≅ β. Draw the rays along those angles and finally draw point F at their intersection.
Notice how the triangles have to say similar even as you drag points around.
4. Use the SSS~ (side-side-side) theorem to build △DEF ~ △ABC. To do that, build the desired ratio (see raw materials). Then build circles with radii of the correct sizes. The circle around point D should have radius distance[A,C]*ratio; the circle around point E should have radius distance[B,C]*ratio. Then draw point F at the point of intersection of those two circles. Finally draw segments DF and EF. Notice how the triangles have to say similar even as you drag points around.
6. Use the SAS~ (side-angle-side) theorem to build △DEF ~ △ABC. This uses a combination of the techniques used in AA and in SSS~. Notice how the triangles have to say similar even as you drag points around.

When you are ready, go back to the lab page.