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3.1 Transforming to a New Level!
Geometry 3.1 Transforming to a New Level! Please Pickup Assignments
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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
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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?
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Create a scenario that will match the situation for how perimeter and area of a rectangle can be used I have an example
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Create a scenario that will match the situation for how perimeter and area of a rectangle can be used
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Create a scenario that will match the situation for how perimeter and area of a rectangle can be used Collaborate (5 Minutes) Turn in when finished Need only one scenario per group
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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 Opposite sides parallel and congruent All angles are congruent and right
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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
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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
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Problem 1: Pomp and Circumstance
Collaborate 5-7 (10 Minutes) Distance Formula 𝑑= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2 Slope Formula 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Area of Rectangle 𝐴=𝑏ℎ 𝐴=𝑙𝑤
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Problem 1: Pomp and Circumstance
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Problem 1: Pomp and Circumstance
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Problem 1: Pomp and Circumstance
#6 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑝𝑎𝑐𝑒=13𝑥13=169 𝑓𝑡 2 𝐴𝑟𝑒𝑎 𝑝𝑒𝑟 𝑃𝑒𝑟𝑠𝑜𝑛= ≈4.69 She can only invite 3 more people to the party
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Problem 2: Maximum Efficiency
Together 1-5
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Problem 2: Maximum Efficiency
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Distance Formula 𝑑= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2 Slope Formula Area 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 A=bh
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The quadrilateral is a square
All 4 sides are congruent Opposite sides are parallel Consecutive sides are perpendicular All 4 angles are right angles
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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?
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Formative Assessment Skills Practice 3.1 Pg. 383-386 (1-8) DUE TODAY
Distance Formula 𝑑= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2 Slope Formula 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1
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