Section 21 Use the Converse of the Pythagorean Theorem

Apuntes

• Subtopic: Using the Converse of the Pythagorean Theorem If $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the shorter sides and $c$ is the length of the longest side, then it is a right triangle. **Example 1: Verify Right Triangles** Tell whether the given triangle is a right triangle. a) 22, 14, 25 b) 9, 3, 15 --- • Subtopic: Classifying Triangles You can use the theorems from this lesson to classify a triangle as acute, right, or obtuse based on its side lengths. **Methods for Classifying a Triangle by Angles Using its Side Lengths** **Theorem 7.2** If $c^2 = a^2 + b^2$, then $m∠C = 90°$ and △ABC is a RIGHT triangle. **Theorem 7.3** If $c^2 < a^2 + b^2$, then $m∠C < 90°$ and △ABC is an ACUTE triangle. **Theorem 7.4** If $c^2 > a^2 + b^2$, then $m∠C > 90°$ and △ABC is an OBTUSE triangle. --- • Subtopic: Review of Triangle Inequality Theorem In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. So, if a triangle has side lengths $a$, $b$, and $c$, then all of these must be true: - $a + b > c$ - $a + c > b$ - $b + c > a$ **Example 2: Can you make a triangle with sides 3, 4, and 8?** $3 + 4 = 7 ≠...