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Orchard Hideout The Central Problem The central problem of this unit concerns two people who have planted an orchard on a circular lot. They want to know how long it will take before the trees grow so large that someone outside the orchard cannot see into the center of the orchard. Answering this question requires students to study circles and coordinate geometry. They develop the formulas for the circumference and the area of a circle, as well as the distance and midpoint formulas, and learn to find the distance from a point to a line. Another theme of the unit is geometric proof. Throughout this unit, students are applying knowledge they acquired in earlier units about similar triangles, trigonometry, and the Pythagorean theorem.
Orchard Hideout Topic Page in your book DAY 1 Orchards and Mini-Orchards . . . . . . . . . . . . . . . . . . . . . . 59Orchard Hideout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 A Geometric Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 Can you answer these question? pdf doc Take a QuizHomework 1: Geometry and a Mini-Orchard . . . . . . . . . .68 DAY 2 POW 2: Equally Wet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Homework 2: Only Two Flowers . . . . . . . . . . . . . . . . . . . . . 71 Do you remember Fireworks? Take this quiz DAY 3 A Perpendicularity Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Homework 3: From Two Flowers to Three . . . . . . . . . . . . 73 Orchard main question Do you want to know about it? DAY 4 More Mini-Orchards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Homework 4: In, On, or Out? . . . . . . . . . . . . . . . . . . . . . . . ..75 DAY 5 Coordinates and Distance . . . . . . . . . . . . . . . . . . . . . . . . .76 The circle Most know Homework 5: Other Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 Symmetry DAY 6 Sprinkler in the Orchard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78 Homework 6:The Distance Formula . . . . . . . . . . . . . . . . . . . .79 The Distance FormulaHow Does Your Orchard Grow? . . . . . . . . . . . . . . . . . . . . . . . 80 Homework 7: A Snack in the Middle . . . . . . . . . . . . . . . . . . . 81 Midpoint FormulaEquidistant Points and Lines . . . . . . . . . 82 Homework 8: Proving with Distance—Part I . . . . . . . . . . . .83 Down the Garden Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Homework 9: Perpendicular and Vertical . . . . . . . . . . . . . . 85 POW 3: On Patrol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86 Homework 10: Proving with Distance—Part II . . . . . . . . . . 88 All About Circles . . . . . . . . . . . . . . . . . . . . . . . . . . .89 Squaring the Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 See Squaring the Circle IIHomework 11: Using the Squared Circle . . . . . . . . . . . . . . . 92 Hexagoning the Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Homework 12: Octagoning the Circle . . . . . . . . . . . . . . . . . .95 Polygoning the Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Homework 13: Another Kind of Bisector . . . . . . . . . . . . . . . .97 Homework 14: Proving Triples . . . . . . . . . . . . . . . . . . . . . . . . 99 POW 4:A Marching Strip . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Homework 15: Orchard Growth Revisited . . . . . . . . . . . . . .102 Cable Complications . . . . . . . . . . . . . . . . . . . . 103 Cable Ready . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Homework 16: Going Around in Circles . . . . . . . . . . . . . . . 105 Homework 17: Daphne’s Dance Floor . . . . . . . . . . . . . . . . .106 Homework 18: Defining Circles . . . . . . . . . . . . . . . . . . . . . . .108 The Standard Equation of the Circle . . . . . . . . . . . . . . . . . . 109 Homework 19: Completing the Square and Getting a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111 Lines of Sight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 The Other Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Homework 20: Cylindrical Soda . . . . . . . . . . . . . . . . . . . . . .115 Lines of Sight for Radius Six . . . . . . . . . . . . . . . . . . . . . . . . . 117 Homework 21: Orchard Time for Radius Three . . . . . . . . . 118 Hiding in the Orchard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Homework 22: Big Earth, Little Earth . . . . . . . . . . . . . . . . . 120 Homework 23: Beginning Portfolios . . . . . . . . . . . . . . . . . . .121 Homework 24:“Orchard Hideout” Portfolio . . . . . . . . . . . 122 Appendix: Supplemental Problems . . . . . . . . . . . . . . . .124 Right and Isosceles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125 The Perpendicular Bisector Converse . . . . . . . . . . . . . . . . . 126 Counting Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Perpendicular Bisectors by Algebra . . . . . . . . . . . . . . . . . . .129 Midpoint Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131 Why Do They Always Meet? . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Inscribed Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 More Inscribed Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135 Angles In and Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Midpoint Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138 Equidistant Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Right in the Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142 Thirty-Sixty-Ninety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 More About Triples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Darts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 The Inscribed Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146 Medians and Altitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147 Hypotenuse Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Not Quite a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .150 Knitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151
Under Construction
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