Suppose you are setting up a banner for your school’s spring festival. You are in charge of attaching the support rope from the top of the banner poles to stakes in the ground.

How can you figure out how long the ropes (shown with dotted lines) have to be?

Study the diagram and write down in your notes what you notice. What might help you figure out the length of the ropes?

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Possible Answer

I see a right triangle formed by a post, the ground between the post and the stake, and the rope. The rope is the hypotenuse of the right triangle. I can measure the height of the post and the distance from the post to the stake. These measurements are the legs of the right triangle. Using the Pythagorean Theorem will tell me the length of the rope. Repeat for the other side.

The observations in the banner example are a set of statements made about the geometric shapes you saw in the picture. As you learn more geometric properties, you notice more and can create more reasonable statements about what you see.