Unit 3 lesson 8 cumulative practice problems
1. this is an invalid proof that all isosceles triangles are similar. explain which step is
invalid and why.
1. draw 2 isosceles triangles abc and def where ac = bc and df = ef.
2. dilate triangle abc to a new triangle a'b'c using center c and scale factor de so
that a'c = b'c = df = ef.
3. translate by directed line segment cf to take a'b'c to a new triangle a"b" f.
since translation preserves distance, a" f = a'c= df and b" f = bc = ef.
4. since a" f = df, we can rotate using center f to take a" to d.
5. since b" f = ef, we can rotate using center f to take b" to e.
6. we have now established a sequence of dilations, translations, and rotations that
takes a to d, b to e, and c to f, so the triangles are similar.