Exploring Similar Triangles and their Properties
What transformation is being shown in this module?
Use the angle measure tool find all three angles in each triangle. What do you notice about corresponding angles?
Try creating triangles that have different angle measure. What do you notice about corresponding angles?
After creating many different triangles how you would you describe these two triangles?
What is a word that we can use to describe two things that are the same in one way, but different in another way?
Adjust your scale factor so that it is equal to 2. What do you notice about the corresponding sides between the two triangles? (Use the distance tool to measure your side lengths.)
Try adjusting the scale factor to different values and for different triangles? What do you notice about the ratios of your corresponding sides?
What is a vocabulary word we could use to summarize our observations that we described in the previous question? The corresponding side lengths are ________.
Write a conjecture about the properties of similar triangles by using the observations you recorded during this activity.
What do you notice about segment BC and segment B'C'?
Use the length tool to find the length of segments AB, BB', AC, CC'. Do you notice any relationships between these lengths, if so describe them. (Hint: Compare the ratios of AB and BB' to AC to CC'.)
Try to moving segment BC to create different triangles, make sure that segments BC and segment B'C' are still parallel. What do you notice about the relationships between the lengths of AB, BB', AC, CC'?
Using the evidence you gathered during this investigation, write a conjecture that summarizes your observations.