1. Pythagorean Theorem and Its Converse

2. Pythagorean Theorem
If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

3. Finding the Length of the Hypotenuse
1. What is the length of the hypotenuse in ∆ABC?
𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑐 2
841 = 𝑐 2
c = 29

4. Simplest Radical Form 20 20
2. Simplify or 10 2 2 5

5. 192 or 192 96 2 2 48 6 8 4 2 3 2 2 2 Simplest Radical Form
3. Simplify 2 48 6 8 4 2 3 2
= 2 ∙ 2 ∙ 2 3
= 8 3 2 2

6. Finding the Length of the Leg
4. What is the value of x? Express your answer in simplest radical form.

7. Converse of the Pythagorean Theorem
If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

8. Pythagorean Triples
A Pythagorean triple is a set of nonzero whole numbers, a, b, and c that always satisfy the equation a² + b² = c².
Some common Pythagorean Triples:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
Keep an eye out for the multiples of these common Pythagorean Triples (ex. 6, 8, 10)

9. Obtuse and Acute Triangles
If the square of the length of the longest side of a triangle is GREATER THAN the sum of the squares of the lengths of the other two sides, then the triangle is OBTUSE.
If the square of the length of the longest side of a triangle is LESS THAN the sum of the squares of the lengths of the other two sides, then the triangle is ACUTE.
𝐶 2 > 𝑎 2 + 𝑏 2
𝐶 2 < 𝑎 2 + 𝑏 2

10. Classifying a Triangle
5. A triangle has side lengths 6, 11, and 14. Is it acute, obtuse, or right?
c² ___ a² + b²
14² ___ 6² + 11²
196 ___
196 ___ 157
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The triangle is obtuse.

11. Homework
Worksheet: The Pythagorean Theorem and Its Converse #’s 1-18