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Geometry and Spatial Sense
Grades 8 – 10
A. Formally define geometric figures.
10.1 Formally define and explain key aspects of geometric figures, including:
A 10.1 07 – 5
A 10.1 04 – 13
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a. interior and exterior angles of polygons
A 10.1 a
b. segments related to triangles (median, altitude, midsegment)
A 10.1 b 03 – 21
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c. points of concurrency related to triangles (centroid, incenter, orthocenter, and
circumcenter)
d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector,
segment,
inscribed angle).
10.2 Recognize and explain the necessity for certain terms to remain undefined, such as
point, line and plane.
10.6 Identify the reflection symmetry of two- and three-dimensional figures.
Identify the rotation symmetry of two- and three-dimensional figures.
10.10 Solve problems involving chords, radii, and arcs within the same circle.
B. Describe and apply the properties of similar and congruent figures; and justify
conjectures involving similarity and congruence.
8.1 Make and test conjectures about characteristics and properties (e.g., sides, angles,
symmetry) of two-dimensional figures and three-dimensional objects.
B 8.1 06 – 37
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B 8.1 03 – 32
8.3 Use proportions in several forms to solve problems involving similar figures
(part-to-part, part-to-whole, corresponding sides between figures).
B 8.3 05 – 23
B 8.3 04 – 36
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B 8.3 08 – 37
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B 8.3 07 – 29
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C. Recognize and apply angle relationships in situations involving intersecting lines,
perpendicular lines, and parallel lines.
8.2 Recognize the angles formed and the relationship between the angles when two lines
intersect
C 8.2 a 07 – 6
C 8.2 a
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C 8.2 a 08 – 42
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Recognize the angles formed and the relationship between the angles when parallel lines
are cut by a transversal.
C 8.2 b 06 – 25
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C 8.2 03 – 1
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C 8.2 05 -1
10.10 Solve problems involving chords, radii, and arcs within the same circle.
D. Use coordinate geometry to represent and examine the properties of geometric figures.
8.1 Make and test conjectures about characteristics and properties (e.g., sides, angles,
symmetry) of two-dimensional figures and three-dimensional objects when graphed.
See Benchmark B
8.4 Represent and analyze shapes using coordinate geometry; e.g., given three vertices
and
the type of quadrilateral, find the coordinates of the fourth vertex.
D 8.4 09 – 23
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D 8.4 08 – 13
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D 8.4 06 – 29
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D 8.4 05 – 41
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D 8.4 05 – 35
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D 8.4 04 – 30
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D 8.4 03 – 38
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D 8.4 03 – 5
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E. Draw and construct representations of two- and three-dimensional geometric objects
using a variety of tools, such as straightedge, compass and technology.
8.6 Draw nets for a variety of:
Prisms
E 8.6 a 06 – 11
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Pyramids
E 8.6 b 06 – 5
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E 8.6 b 09 – 7
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E 8.6 b 03 – 13
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Cylinders
Cones.
Other
E 8.6 08 – 4
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10.4 Construct (using compass and straightedge or dynamic geometry software)
right triangles
equilateral triangles
parallelograms
trapezoids
rectangles
rhombuses
squares
kites
10.5 Construct congruent using tools, such as compass, straightedge, and protractor or
dynamic geometry software.
Construct similar figures using tools, such as compass, straightedge, and protractor
or dynamic geometry software.
10.7 Perform reflections using compass and straightedge constructions and dynamic
geometry
software.
Perform rotations using compass and straightedge constructions and dynamic
geometry
software.
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F. Represent and model transformations in a coordinate plane and describe the results.
8.5 Draw the results of the following transformations of objects in the coordinate plane,
and determine properties that remain fixed ( e.g., lengths of sides remain the same
under translations)
Translation
F 8.5 a 07 – 37
F 8.5 09 – 18
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F 8.5 a 04 – 10
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Reflections
F 8.5 b 07 – 42
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F 8.5 b 09 – 40
F 8.5 b 05 – 6
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F 8.5 b 03 – 28
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Rotations
F 8.5 08 – 34
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Dilations
9.8 Derive coordinate rules for the following transformations of geometric figures in the
coordinate plane.
Translation
Reflections
Rotations
Dilations
9.9 Show and describe the results of combinations of translations, reflections and
rotations (compositions); e.g., perform compositions and specify the result of a
composition as the outcome of a single motion, when applicable.
G. Prove or disprove conjectures and solve problems involving two- and three-dimensional
objects represented within a coordinate system.
9.3 Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance
formulas to show that a quadrilateral is a parallelogram
G 9.3 06 – 40
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H. Establish the validity of conjectures about geometric objects, their properties and
relationships by counter-example, inductive and deductive reasoning, and critiquing
arguments made by others.
8.1 Make and test conjectures about characteristics and properties (e.g., sides, angles,
symmetry) of two-dimensional figures and three-dimensional objects. See Benchmark
B
H 8.1 04 – 33
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H 8.1 03 – 7
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10.3 Make, test and establish the validity of conjectures about geometric properties and
relationships using counterexample, inductive and deductive reasoning, and
paragraph or two-column proof, including: (This list is extensive and needs to be
mapped separately)
a. prove the Pythagorean Theorem
b. prove theorems involving triangle similarity and congruence
c. prove theorems involving properties of lines, angles, triangles and quadrilaterals
d. test a conjecture using basic constructions made with a compass and straightedge
or technology.
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10.10 Solve problems involving chords, radii, and arcs within the same circle.
I. Use right triangle trigonometric relationships to determine lengths and angle measures.
9.1 Define the basic trigonometric ratios in right triangles:
Sine
Cosine
Tangent.
9.2 Apply proportions to solve problems involving missing lengths and angle sizes in
similar figures.
I 9.2 09 – 29
Apply right triangle trigonometric ratios to solve problems involving missing lengths
and angle sizes in similar figures.
I 9.2 b 09 – 36
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I 9.2 b 03 – 40
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