The classic in-class activity for teaching induction is to give the students a sequence and ask for the next two elements in the sequence. For example 1, 1, 2, 3, 5, __, __ or 1, 4, 9, 16, __, __ or 1, 2, 6, 7, 21, __, __. To make the activity more geometric, you can draw a square with one quarter shaded in (e.g., the upper left quadrant) that goes through repeated sequences or rotations and flips. It is important to always ask for the next two steps in the sequence, to prevent guessing. Make it clear to the students that guessing the next step in a sequence is inductive and not deductive.
For homework and test sequences, it is possible to use more complex geometric shapes and to present multiple choices for the answer--something that would be confusing and time consuming on the board. With these examples, shapes can rotate, add parts, delete parts and change in other ways. Give these sorts of sequences for homework and test activities as a good way to prepare students to take standardized tests. If you want to make the exercises more like standardized tests, do not just choose the wrong answers at random. Go through the sequence and make the most likely mistakes, and give the solution for each mistake as one of the incorrect choices. These puzzles illustrate the roles of both inductive and deductive reasoning in geometry. Induction suggests the answer and deduction verifies the selection.
Proving that the formula, Area = 1/2 X Base X Height, gives the correct area for a triangle takes several deductive steps. To get an idea of which deductive steps to take, you'll notice that each square or rectangle can be cut into two triangles by cutting along the diagonal. Perhaps this is where the 1/2 comes from, because the area of these quadrilaterals is Area = Base X Height. This is inductive reasoning, but it can be used to direct the deductive reasoning that proves the hypotheses. Activities that give an inductive justification for each deductive proof shows students the creative reasoning behind what often appears to be a mechanical process.