Exploring Pythagorean Theorem and Converse in Geometry

Uncover the mysteries of the Pythagorean Theorem and its converse in this educational content. Discover how to apply the theorem to find hypotenuses, determine Pythagorean triples, and verify right triangles. Engage in solving geometric problems involving triangles, lengths, and distances with practical examples provided. Dive into the world of triangles, squares, and geometric relationships to enhance your mathematical understanding.

• Pythagorean Theorem
• Geometry
• Triangles
• Converse
• Educational

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Uploaded on Nov 13, 2024 | 0 Views

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1. Objectives: 1) To use the Pythagorean Theorem. 2) To use the converse of the Pythagorean Theorem.

2. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a + b = c

3. Is a set of nonzero whole satisfy the equation a + b = c Examples: (most common) 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 whole numbers a, b, c that **If you multiply each number in a Pythagorean triple by the same whole number, the three numbers is a new triple.

4. A right triangle has legs of length 16 and 30. Find the hypotenuse. Do the lengths form a Pythagorean triple?

5. Find the value of x. Leave your answer in simplest radical form. 3 7 x

6. The hypotenuse if a right triangle has length 12. One leg has length 6. Find the length of the other leg. Leave your answer in simplest radical form.

7. A baseball diamond is a square with 90 ft. sides. Home plate and second base are at opposite vertices of the square. About how far is home plate from second base?

8. Find the area of the triangle.

9. If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

10. 9 18 5

11. Classwork Handed-In Page 360 #1-12, 16, 18-23