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Unit Packet - Pythagorean Theorem

Some helpful definitions:

Theorem: A statement that is proven to be true by mathematicalarguments. It is often times stated as an “If...then…” statement.

ex. If it is raining, then the ground is wet.

Converse: Switches the “If...then…” parts of a statement Statement: If it is raining, then the ground is wet. Converse of statement: If the ground is wet, then it is

raining.

Mathematical Argument: An argument which convinces other people that something is true. Often times cites theorems.

Hypotenuse: The longest side of a right triangle. It is opposite the right angle.

Legs of a triangle: Either of the sides in a right triangle that are opposite an acute angle (the two shorter sides in a right triangle)

Part B: Using the Pythagorean TheoremUse the Pythagorean theorem to determine whether or not each of the following is a right triangle. Explain your reasoning.

1.

2. A triangle with sides 8, 15, and 16.

3.

Follow-Up Question:You are told that two sides of a right triangle are 5 and 12. How many right triangles can you make with sides of 5 and 12?

Part C: Exploring the Pythagorean Theorem

On the southeast corner of the Mission Viejo Park, there is a garden walk. It is marked off in red in the drawing below. Side C, the hypotenuse of the triangle, shows the row along which flowers will be planted.

a) If side a measures 90 feet and side b measures 120 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work and make a mathematical argument to explain your reasoning.

b) Let square C represent the stage for a concert. The front of the stage, side C, is 50 feet long. A 40-foot rope runs along the side of square B. A 30-foot rope runs along the side of square A. Is the roped off area, triangle ABC, a right triangle? Explain.

Part D: Applying the Pythagorean TheoremSolve the following problems with your partner:

1. Ally and Bob are looking to buy a new flatscreen TV to put in their bedroom. The TV that they found is 10 feet tall and 24 feet wide. What will be the length of the diagonal of the TV?

2. A firefighter is trying to rescue a woman from her third floor apartment building by having her escape through the window. The firefighter brings with him a 10-meter ladder, and that ladder is perfectly positioned so that it reaches the woman’s window. The base of the ladder was calculated to be 5 meters from the edge of the building. What is the height of the woman’s window?Hint: Apply the image to the word problem.