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KUD Organizer
Course: Geometry
Unit: Measurements of Two-Dimensional Shapes and Figures
Approximate Days: 180 days
STANDARDS:
2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
2.3.HS.A.9 Extend the concept of similarity to determine arc lengths and areas of sectors of circles.
2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context.
2.3.HS.A.8 Apply geometric theorems to verify properties of circles.
2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.
UNDERSTAND:
Perimeter and area of geometric shapes can be described by equations, making algebraic manipulation into a tool for geometric
understanding, modeling and proof.
The range of models that we can create and analyze is constrained by the limitations of our mathematical, statistical and technical
skills and our ability to recognize significant variables and relationships among them.
Some geometric relationships can be described and explored as functional relationships.
Real world situations are organized and labeled for analysis, and formulating flexible geometric models and analyzing them is a
creative process.
KNOW:
DO:
How to use and/or compare measurements
of angles.
Use properties of angles formed by intersecting lines to find the measures of missing
angles.
How to use procedures to determine or
describe measures of perimeter,
circumference, and/or area. (May require
conversions within the same system.)
Use properties of angles formed when two parallel lines are cut by a transversal to
find the measures of missing angles.
Describe how a change in
one dimension of a 2‑dimensional figure
affects other measurements of that figure.
Find the measurement of a missing length, given the perimeter, circumference, or
area.
Apply probability to practical situations.
Estimate area, perimeter, or circumference of an irregular figure.
Find the side lengths of a polygon with a given perimeter to maximize the area of the
polygon.
Develop and/or use strategies to estimate the area of a compound/composite figure.
Find the area of a sector of a circle.
Describe how a change in the linear dimension of a figure affects its perimeter,
circumference, and area (e.g., How does changing the length of the radius of a circle
affect the circumference of the circle?).
Use area models to find probabilities.
KEY VOCABULARY:
base, height, radius, apothem, angle addition postulate, assumptions, complementary, supplementary angles, linear pair
(postulate),Theorems: complements/supplements of congruent angles are congruent, right angles are congruent, vertical angles,
angle bisector, quadrisect, Theorems: vertical angles are congruent, perpendicular lines form 4 right angles, [alternate-interior/
alternate -exterior/corresponding/same-side interior] angles alternate-interior angles ≅ then parallel lines postulate, Theorems:
corresponding angles ≅ then parallel, alternate -exterior angles ≅then parallel, same-side interior angles supplementary then
parallel, polygonal region, area, perimeter, Area Postulate, Area Addition Postulate, circumference = πd or 2πr , area = πr2, sector,
Proportions of Circles
geometric probability
𝑚∠𝐴𝐵𝐶
360°
=
̂
𝑚𝐴𝐶
360°
=
𝑙𝑒𝑛𝑔𝑡ℎ𝐴𝐶
̂
2𝜋𝑟
=
𝑎𝑟𝑒𝑎𝑠𝑒𝑐𝑡𝑜𝑟
𝜋𝑟 2