Transcript 3.1 Transformations and Areax

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