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Transcript
GEOMETRY
Alabama Course of Study: Mathematics
Bulletin 2003, No. 4 - Effective 2004 - 2005 School Year
COS
Students will:
Geometry
Geometry A
1
Determine the equation of a line parallel or perpendicular
to a second line through a given point.
x
x
2
Justify theorems related to pairs of angles, including
angles formed by parallel and perpendicular lines, vertical
angles, adjacent angles, complementary angles, and
supplementary angles.
x
x
Geometry B
Ex: proving vertical angles congruent
Verify the relationships among different classes of
polygons by using their properties.
3
x
Ex: showing that a square has all the properties of both a
rectangle and a rhombus
x
* Determining the missing lengths of sides or measures of
angles in similar polygons
x
Determine the measure of interior and exterior angles
associated with polygons.
x
* Verifying the formulas for the measures of interior and
exterior angles of polygons inductively and deductively.
x
4
x
Solve real-life and mathematical problems using
properties and theorems related to circles, quadrilaterals,
and other geometric shapes.
5
6
7
x
x
* Determining the equation of a circle given its center and
radius
x
x
Apply the Pythagorean Theorem to solve application
problems, expressing answers in simplified radical form or
as decimal approximations, using Pythagorean triples
when applicable.
x
x
Use the ratios of the sides of special right triangles to find
lengths of missing sides.
x
* Deriving the ratios of the sides of 30-60-90 and 45-4590 triangles
x
x
Ex: finding the center of a solid wooden wheel using the
perpendicular bisectors of two chords
x
x
8
9
Deduce relationships between two triangles, including
proving congruence or similarity of the triangles from
given information, using the relationships to solve
problems and to establish other relationships.
x
* Determining the geometric mean to find missing lengths
in right triangles
x
Use inductive reasoning to make conjectures and
deductive reasoning to justify conclusions.
x
x
* Recognizing the limitations of justifying a conclusion
through inductive reasoning
x
x
Find the missing measures of sides and angles in right
10 triangles by applying the right triangle definitions of sine,
cosine, and tangent.
11 Determine the areas and perimeters of regular polygons,
including inscribed or circumscribed polygons, given the
coordinates of vertices or other characteristics.
12
x
Apply distance, midpoint, and slope formulas to solve
problems and to confirm properties of polygons.
x
x
x
x
x
x
x
x
x
Ex: finding the area of a rectangle given the coordinates
of its vertices, showing that the median of a trapezoid is
half the sum of the bases
13
Identify the coordinates of the vertices of the image of a
given polygon that is translated, rotated, reflected, or
dilated.
Ex: rotating a triangle a given number of degrees around
a specific point, comparing the vertices of the image and
preimage
Classify polyhedrons according to their properties,
including the number of faces.
14 Ex: identifying a polyhedron having 6 vertices and 12
edges
* Identifying Euclidean solids
15 Calculate measures of arcs and sectors of a circle from
given information.
x
x
x
x
x
Ex: finding the area of a sector given its arc length and
radius, finding the arc length of a sector given its area and
radius, finding the area or arc length given the measure of
the central angle and the radius
Calculate surface areas and volumes of solid figures,
including spheres, cones, and pyramids.
x
x
* Developing formulas for surface area and volume of
spheres, cones, and pyramids
x
x
16 * Calculating specific missing dimensions of solid figures
from surface area or volume
x
x
x
x
* Determining the relationship between the surface areas
of similar figures and volumes of similar figures
Analyze sets of data from geometric contexts to
determine what, if any, relationships exist.
Ex: Collect data and create a scatterplot comparing the
perimeter and area of various rectangles. Determine
whether a line of best fit can be drawn.
x
17 * Distinguishing between conclusions drawn when using
deductive and statistical reasoning
x
x
* Calculating probabilities arising in geometric contexts
Ex: finding the probability of hitting a particular ring on a
dart board whose rings are formed by equally spaced
concentric circles
x
18 Construct with precision a circle graph to represent data
from given tables or classroom experiments.
x
x