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Chapter R Section 3: Geometry Essentials

Chapter R Section 3: Geometry Essentials. In this section, we will… Use the Pythagorean Theorem and its converse Know and use geometry formulas. In a right triangle, with c = hypotenuse

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Chapter R Section 3: Geometry Essentials

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  1. Chapter R Section 3: Geometry Essentials • In this section, we will… • Use the Pythagorean Theorem • and its converse • Know and use geometry formulas

  2. In a right triangle, with c = hypotenuse Example: In a right triangle, the length of one side is 5 feet and the length of the hypotenuse is 13 feet. What is the length of the remaining side? R.3 Geometry Essentials: Use the Pythagorean Theorem and its Converse

  3. Converse of the Pythagorean Theorem: In a triangle, if the square of the length of one side equals the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. Example: Determine if a triangle whose sides are lengths 5, 4 and 7 is a right triangle. Example: Determine if a triangle whose sides are lengths 8, 15 and 17 is a right triangle. R.3 Geometry Essentials: Use the Pythagorean Theorem and its Converse

  4. A Pythagorean Triple or perfect triple is a list of three positive integers: a, b, c that satisfy the Pythagorean Theorem R.3 Geometry Essentials: Use the Pythagorean Theorem and its Converse

  5. Geometry Formulas to Know Rectangle Perimeter = sum of all sides or Rectangular Box R.3 Geometry Essentials: Know and Use Geometry Formulas

  6. Geometry Formulas to Know Triangle Perimeter = sum of all sides Circle *To minimize rounding-errors we will use the button on our TI R.3 Geometry Essentials: Know and Use Geometry Formulas

  7. Geometry Formulas to Know Sphere Right Circular Cylinder R.3 Geometry Essentials: Know and Use Geometry Formulas

  8. Example: How many revolutions will a circular disk with diameter of 4 feet have completed after it has rolled 20 feet. Round your result to the nearest tenth. R.3 Geometry Essentials: Know and Use Geometry Formulas

  9. Example: A device is in the shape of a semicircle on top of a triangle (the device is flat). How many square centimeters of copper is required to make the device if the height of the triangle is 6 cm and the base is 4 cm. Round your result to the nearest hundredth. R.3 Geometry Essentials: Know and Use Geometry Formulas

  10. Example: Find the exact area of the shaded region: 2 meters 2 meters R.3 Geometry Essentials: Know and Use Geometry Formulas

  11. Example: Find the volume and the surface area of a right circular cylinder with radius of nine inches and a height of eight inches. Round your results to the nearest hundredth. volume: surface area: R.3 Geometry Essentials: Know and Use Geometry Formulas

  12. Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp. 30-35 Homework: pp. 36-38 #13, 15, 21, 27-37 odds, 45, 49 R.3 Geometry Essentials

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