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Why is this concept useful?: The hypotenuse is the longest side of a right triangle. We use the Pythagorean Theorem to find the missing side length of a right triangle.
Where does this concept fit into the curriculum?: Grade 8

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How can we use the concept:

The Pythagorean Theorem states that a2 + b2 = c2 , where a and b represent the legs of the right triangle, and c represents the hypotenuse. Sides a and b are always the shortest side of the right triangle, and c (the hypotenuse) is always the longest side. The hypotenuse is opposite the right angle.

Sample Math Problems

1. Which side of the triangle is the hypotenuse?

Solution:
Sides QR and RP are the legs.
Side QP is the hypotenuse.

2. What is the measure of BC?

Solution:

\begin{array}{l} a^{2} +b^{2} =c^{2}\\ 28^{2} +45^{2} =c^{2}\\ 2809=c^{2}\\ \sqrt{2809} \ =\ c\\ c=\sqrt{2809} \ units \end{array}

3. What is the measure of LM?

Solution:

\begin{array}{l} a^{2} +b^{2} =c^{2}\\ a^{2} +40^{2} =50^{2}\\ a^{2} =900\\ a=30\ units \end{array}

4. What is the measure of KL?

Solution:

\begin{array}{l} a^{2} +b^{2} =c^{2}\\ a^{2} +10^{2} =26^{2}\\ a=24\ units \end{array}

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