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Geometry 3.1 Transforming to a New Level! 3.1 Using Transformations to Determine Area • Objectives • Determine the areas of squares on a coordinate plane • Connect transformations of geometric figures with number sense and operations • Determine the area of rectangles using transformations Explain the rationale behind your decision? What “BIG” ideas are needed to show that ABCD is a rectangle? What formulas are needed to prove your decision? Create a scenario that will match the situation for how perimeter and area of a rectangle can be used I have an example Create a scenario that will match the situation for how perimeter and area of a rectangle can be used Create a scenario that will match the situation for how perimeter and area of a rectangle can be used Collaborate (5 Minutes) Turn in on round table when finished Need only one scenario per group Problem 1: Pomp and Circumstance • Collaborate 1-4 (7 Minutes) • Properties of Squares • Quadrilateral • All sides congruent • All angles congruent and right • Properties of Non-Square Rectangles • Quadrilateral • Opposite sides parallel and congruent • All angles are congruent and right Problem 1: Pomp and Circumstance • #3 • Need to show 4 right angles • Use slopes of lines • Opposite reciprocal slopes determine perpendicular lines • Need to find the length of all sides • Use the distance formula to find a length Problem 1: Pomp and Circumstance • #4: What do we need to know? • Need to know the area of the room • Need to know how to find the area of a rectangle/square • Can divide the area of the quadrilateral by the space taken up per person Problem 1: Pomp and Circumstance • Collaborate 5-7 (10 Minutes) • Distance Formula 𝑑= • Slope Formula 𝑥2 − 𝑥1 2 + 𝑦2 − 𝑦1 𝑦2 − 𝑦1 𝑚= 𝑥2 − 𝑥1 • Area of Rectangle 𝐴 = 𝑏ℎ 𝐴 = 𝑙𝑤 2 Problem 1: Pomp and Circumstance Problem 1: Pomp and Circumstance Problem 1: Pomp and Circumstance #6 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑝𝑎𝑐𝑒 = 13𝑥13 = 169 𝑓𝑡 2 169 𝐴𝑟𝑒𝑎 𝑝𝑒𝑟 𝑃𝑒𝑟𝑠𝑜𝑛 = ≈ 4.69 36 She can only invite 3 more people to the party Formative Assessment • We will be on computers tomorrow and Friday 3.1 Using Transformations to Determine Area • Objectives • Determine the areas of squares on a coordinate plane • Connect transformations of geometric figures with number sense and operations • Determine the area of rectangles using transformations Problem 2: Maximum Efficiency • Together 1-5 Problem 2: Maximum Efficiency Distance Formula 𝑑 = 𝑥2 − 𝑥1 Slope Formula 𝑦 −𝑦 𝑚 = 𝑥2−𝑥1 2 1 2 + 𝑦2 − 𝑦1 2 Area A=bh The quadrilateral is a square All 4 sides are congruent Opposite sides are parallel Consecutive sides are perpendicular All 4 angles are right angles Summation • What are the properties of a square? • What are the properties of a rectangle? • What formulas do we need to prove a figure is a square or a rectangle? Formative Assessment • Skills Practice 3.1 • Pg. 383-386 (1-8) DUE TODAY • Distance Formula 𝑑= 𝑥2 − 𝑥1 • Slope Formula 2 + 𝑦2 − 𝑦1 𝑦2 − 𝑦1 𝑚= 𝑥2 − 𝑥1 2