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Warm-up: Do this on a separate piece of paper. Take the paper home with you to study. Quiz Target 8D next class.

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem Target 9A. I CAN use the converse of the Pythagorean Theorem to classify a right, acute or obtuse triangle. Page 244 Target 9B. I CAN solve and identify the parts of a right triangle.

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem Theorem 9-1 The Pythagorean Theorem. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs. Page 244 Notes Ex: Find the value of x.

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem Pythagorean Triple. A Pythagorean Triple is a set of three positive integers (whole numbers) a, b and c which satisfy the Pythagorean Theorem. Page 244

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem Notes Ex: Find the value of x. Then tell whether the side lengths form a Pythagorean Triple. a) b) Page 244 Yes, the lengths are a Pythagorean triple, 5, 12, 13. Yes, the lengths are a Pythagorean triple, 30, 40, 50.

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem Theorem 9-2 Converse of The Pythagorean Theorem. If the square of the length of the longest 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. Notes Ex: A triangle has side lengths 15, 17, & 20 is it a right triangle? Page 245

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem Page 245 Notes Ex: Verify that the segments form a triangle. Is the triangle acute or obtuse? a) 16, 20, 23 b) 15, 8, 23

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem In Exercises 1-6, find the value of x. Then tell whether the side lengths form a Pythagorean Triple. Page 246 Yes, the lengths are a Pythagorean triple, 81, 108, 135 or 3(27), 4(27), 5(27). No, the lengths are not a Pythagorean triple. Yes, the lengths are a Pythagorean triple, 15, 20, 25 or 3(5), 4(5), 5(5).

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem In Exercises 1-6, find the value of x. Then tell whether the side lengths form a Pythagorean Triple. Page 246 Do these on your own, I’ll give you the answers next class. Check your answers in your table group.

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem Page 246 Home School (Biking south and then east ) = = 1.7 miles (Biking diagonal) 2 = (1.2) 2 +(0.5) 2 = = SQUARE ROOT 1.69 = 1.3 miles How many fewer miles would you have biked? 1.7 – 1.3 = 0.4 miles

POINTS, LINES AND PLANES Geometry 9-1 The Pythagorean Theorem In Exercises 8 and 9, verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse? Page 246

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