The Pythagorean theorem states that: In any **right triangle**, the area of the square whose side is the hypotenuse (the side opposite the **right** angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a **right** angle).

Thereof, how do you find the hypotenuse of a right triangle?

The **hypotenuse** is always opposite the **right** angle and it is always the longest side of the **triangle**. To **find** the length of leg a, substitute the known values into the Pythagorean Theorem. Solve for a^{2}.

How can you use the converse of the Pythagorean theorem to tell if a triangle is a right triangle?

**Pythagorean** Thereom **converse**: **If** the square of one side of a **triangle** is equal to the sum of the squares of the other two sides, then the **triangle is a right triangle**. Write the **Converse Theorem** and complete the proof in your Journal.

How do you know if three sides make a triangle?

The sum of the **lengths** of any two **sides** of a **triangle** is greater than the **length** of the third **side**. **If** you take the three **sides** of a **triangle** and add them in pairs, the sum is greater than (not equal to) the third **side**. **If** that is not true, then it is not possible to construct a **triangle** with the **given side lengths**.

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