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Bellringer

Bellringer. Simplify the radical. The Pythagorean Theorem and its Converse. 7-2. 7-2 The Pythagorean Theorem. Objectives Use the Pythagorean Theorem Use the converse of the Pythagorean Theorem. Theorem 7-4.

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Bellringer

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  1. Bellringer • Simplify the radical.

  2. The Pythagorean Theorem and its Converse 7-2

  3. 7-2 The Pythagorean Theorem • Objectives • Use the Pythagorean Theorem • Use the converse of the Pythagorean Theorem

  4. Theorem 7-4 • Pythagorean Theorem In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse.

  5. Example 1 Find the Length of the Hypotenuse • CONSTRUCTIONAnita and her father are building an addition on their home. A section of a new wall is 6 feet wide and 8 feet high. The are installing a diagonal brace to make sure that the vertical boards are perpendicular to the horizontal boards. How long does the brace need to be?

  6. Work it • Example 2 Find the Length of a Leg. Find x. 16

  7. Theorem 7.5 • Converse of the Pythagorean Theorem If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

  8. Verify a Triangle is a Right Triangle • COORDINATE GEOMETRY Verify that XYZ is a right triangle.

  9. Pythagorean triple • A Pythagorean triple is three whole numbers that satisfy the Pythagorean theorem. • 3,4,5 • 5,12,13 • 7,24,25

  10. Work it • Determine whether each set of measures can be the sides of a right triangle. Then state whether they form a Pythagorean triple. • 10, 15, 18 • 24, 45, 51

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