Pythagorean Theorem

1. Do the lengths 3, 4, and 5 make a perfect triangle? Prove your answer using the Pythagorean Theorem.

   Hint

   $a^2 + b^2 = c^2$

   Solution

   Yes

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2. Do the lengths 5, 6, 9 make a perfect triangle? Prove your answer using the Pythagorean Theorem.

   Hint

   $a^2 + b^2 = c^2$

   Solution

   No

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3. Find the side length of $c$ when $a = 5 \textit{ units}$ and $b = 12 \textit{ units}$.

   Hint

   $a^2 + b^2 = c^2$

   Solution

   $13 \textit{ units}$

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4. What is the Pythagorean Theorem?

   Hint

   One angle must be $90 ^{\circ}$

   Solution

   $a^2 + b^2 = c^2$

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5. How many degrees are in a Right Triangle?

   Solution

   $90 ^{\circ}$

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6. In a Right Triangle, what is the name of the side across from the Right Angle?

   Solution

   Hypotenuse

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7. Which of these numbers is irrational?

   Solution

   $\sqrt{2}$

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8. What is the name of an angle smaller than a Right Angle?

   Solution

   Accute

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9. What is the name of an angle larger than a Right Angle?

   Solution

   Obtuse

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10. What is the length of side $a$ if $b=12 \textit{ units}$ and $c=15 \textit{ units}$?

    Solution

    $9 \textit{ units}$

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