Using everything you have learned from class, be a Pythagorean Detective outlining all of the evidence you can for the following questions. Some clues that you may want to remember include: !

* Pythagorean Theorem: The area of the squares around the two legs of a right angle triangle, add up to the area of the square around the hypotenuse.

* The theorem only works for right angle triangles. The hypotenuse is the longest length of the triangle.

* A pythagorean triple is a set of 3 side-lengths that are multiples of the smallest whole-number side lengths that satisfy a right angle triangle: 3,4,5.

1. Show all of your work to find the missing lengths for the right angle triangle below. Are you looking for the hypotenuse? Do you need to approximate the side-length?

2. A track star by the name of Imma Runr practices by running diagonally across her rectangular back yard. How many times will she have to run to

reach her goal of 1 km? Hrm... how many meters are in a kilometer?

Finding Clues with Pythagoras Name: Date: Class:

6 cm

8 cm

?4 cm

12 cm ?

3 cm 5 cm

6 cm 10 cm

?

12 m

16 m

3. The SELFIE POLE promises to be a popular 2014 holiday gift. The instructions recommend that users always hold the pole such that the camera is at eye level, at least 24 cm away from your face. Your hand must hold the pole at least 18 cm down from eye-level. How long is the pole in cm?

4. Mia has said that a triangle that has side lengths that measure 7 cm, 11 cm and 15 cm is a right angle triangle. Can you help her decide if her thinking is correct? Provide proof.

5. Ready for a doozy of a question? In a room shaped like a rectangular prism, with dimensions 30 m, 12 m, and 12 m, a spider is located in the middle of one wall one foot away from the ceiling. A fly is in the middle of the opposite wall one foot away from the floor. If the fly remains in one spot, what is the shortest total distance the spider must crawl along the walls, ceiling, and floor in order to capture the fly?