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Program of Study for High School Mathematics

GEOMETRY / PART II (314336)
Grade: 11-12
Prerequisite: Geometry / Part I
Credit: One

Overview

Required Basal Textbooks

I. Reasoning and Proof (Review - See Geometry / Part I POS)

II. Other Polygons (Geometry / Part II)

III. Lines & Angles (Review - See Geometry / Part I POS)

IV. Circles (Geometry / Part II)

V. Triangles (Review - See Geometry / Part I POS)

VI. Three-Dimensional Geometry (Geometry / Part II)

VII. SOL Assessment Preparation (FCPS Geometry SOL Review Guide)


Overview

Students investigate properties of quadrilaterals, other polygons, circles, and three-dimensional figures using inductive and deductive reasoning. Topics include area, perimeter, symmetry, reflections, rotations, translations, arc length, circumference, secants, tangents, volume, polyhedra, and surface area. Vectors, algebra, and technologies are used as tools to solve geometry problems. This course includes and integrated review of the Geometry/Part I topics needed for the Geometry SOL test. [This course has an end-of- course Standards of Learning test.]

All of the Geometry Virginia Standards of Learning are addressed in this course. The number in parentheses following each Essential Knowledge and Skill refers to the related SOL objective. Required Program of Studies objectives that are not addressed in the Geometry Virginia SOL are in italics type.

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Required Basal Textbooks
  • Price, Cummins, et al. Glencoe Geometry: Concepts and Applications. Glencoe/McGraw-Hill. 2001.
  • Burrill, et al. Glencoe Geometry: Integration, Applications, Connections. Glencoe/ McGraw-Hill. 2001.
  • Larson, Boswell, & Stiff. McDougal-Littell Geometry. McDougal-Littell. 2001/2004.

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I. Reasoning and Proof

II. Other Polygons

Benchmark

Students investigate a variety of polygons to determine measures and properties,

Including fundamental relationships between angles and segments.

Key Terms

apothem hexagon pre-image
area image radius
circumscribed polygon inscribed polygon reduction
composition interior angle reflection
concave or nonconvex isometry regular polygon
convex line symmetry rotation
decagon mapping rotational symmetry
degree n-gon scale factor
diagonal nonagon tessellation
dodecagon pentagon transformation
enlargement perimeter translation
exterior angle point symmetry translational symmetry
heptagon polygon

Essential Knowledge and Skills/Indicators

  1. Identify, name, and classify polygons. (G.9)
  2. Examine pre-image and image figures in the coordinate plane and determine whether a translation, reflection, or rotation has occurred. (G.2)
  3. Use inductive reasoning to develop a formula for finding the sum of the measures of the interior angles of a convex polygon and the measure of each interior angle of a regular polygon. (G.9)
  4. Investigate the sum of the measures of the exterior angles of any convex polygon and the measure of each exterior angle of a regular convex polygon. (G.9)
  5. Use tessellations and tiling problems to make connections to art, architecture, construction, and the sciences. (G.9)
  6. Investigate symmetry. (G.2)
  7. Determine if a geometric figure has point symmetry, line symmetry, rotational symmetry, translational symmetry, or no symmetry, and justify the conclusion. (G.2)
  8. Define parallelogram. (G.8)
  9. Use inductive reasoning to make conjectures about the properties of parallelograms. (G.8)
  10. 10) Prove the properties of parallelograms using deductive arguments as well as algebraic or coordinate methods. (G.8)
  11. Verify the converse of the properties of parallelograms and use the converses to prove that a quadrilateral is a parallelogram. Coordinate methods may involve using slope to show that lines are parallel or perpendicular. (G.8)
  12. Identify rhombi, squares, and rectangles as special parallelograms and prove their properties using deductive arguments as well as algebraic and coordinate methods. (G.8)
  13. Identify trapezoids and isosceles trapezoids. Prove their properties using deductive arguments as well as algebraic and coordinate methods. (G.8)
  14. Identify kites and prove their properties using deductive arguments as well as algebraic and coordinate methods. (G.8)
  15. Given the areas of similar geometric figures, investigate the effect on the constant of proportionality of changing one dimension (multiplying by a constant). (G.14)
  16. Generalize the change and use the generalization to solve practical problems. (G.14)

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III. Lines & Angles

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IV. Circles

Benchmark

Students investigate properties of circles focusing on relationships among angles, arcs, lines, and chords.

Key Terms

arc

degrees

radians

arc length

diameter radius

area

inscribed angle

secant

center intercepted arc sector
central angle limit segment of a circle
chord major arc semicircle
circumference minor arc tangent
concentric unit circle

Essential Knowledge and Skills/Indicators

  1. Define the term circle. Differentiate between a circle and a circular region. (G.10)
  2. Use the vocabulary associated with circles. (G.10)
  3. Describe ways that circles intersect. (G.10)
  4. Explore and state properties of tangents. (G.10)
  5. Measure central angles, inscribed angles, and arcs of circles directly and indirectly. Generalize the relationship between angle measure and arc measure. (G.10)
  6. Investigate properties of chords and arcs of circles. (G.10)
  7. Measure angles formed by tangents, chords, and secants directly and indirectly. Generalize the relationship between angle measure and arc measure. (G.10)
  8. Find the area of a sector and the area of a segment of a circle. (G.10)
  9. Use the properties of angles, arc, segments, and lines associated with circles to solve practical problems involving circles. Look at applications in art, construction, architecture, and the sciences. (G.10)

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V. Triangles

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VI. Three-DImension Geometry

Benchmark

Students investigate polyhedrons by extending concepts of plane geometry to three dimensions.

Key Terms

base edge

base of a solid

cone

cube

cylinder

dihedral angle
dodecahedron edge face
hemisphere hexahedron icosahedron
lateral edge net oblique solid
octahedron Platonic solids polygon
polyhedron prism pyramid
radius regular polygon right solid
scale factor slant height sphere
surface (total) area tetrahedron vertex
volume

Essential Knowledge and Skills/Indicators

  1. Sketch polyhedrons and identify relevant parts. (G.12)
  2. Use properties of three-dimensional objects to make models. (G.12)
  3. Make a model of a three-dimensional figure from a two-dimensional drawing. (G.12)
  4. Make a two-dimensional representation of a three-dimensional object. (G.12)
  5. Use scale drawings, perspective drawings, blueprints, or computer drawings as models of three-dimensional objects to solve problems. (G.12)
  6. Identify a three-dimensional object from different positions such as the top view, side view, and front view. (G.12)
  7. Use the appropriate formulas to find the surface area of cylinders, prisms, pyramids, cones, and spheres. (G.13)
  8. Use the appropriate formulas to calculate the volume of cylinders, prisms, pyramids, cones, and spheres. (G.13)
  9. Solve practical problems involving surface area and volume of cylinders, prisms, pyramids, cones, and spheres as well as combinations of three-dimensional figures. (G.13)
  10. Use proportions to compare surface area and volumes of three-dimensional geometric figures. (G.14)
  11. Describe how a change in one measure affects other measures of an object. (G.14)
  12. Solve practical problems involving similar objects. (G.14)
  13. Explore results of oblique cuts on traditional solids.

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VII. SOL Assessment Preparation
  • See FCPS Geometry SOL Review Guide

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David Van Vleet
Mathematics Specialist
DVanVleet@fcps.edu
703-846-8650

Donald Lacey Instructional Center
3705 Crest Drive
Annandale, VA 22003


Last Updated
9/9/2004

Contact
Yvonne Griggs
Yvonne.Griggs
@fcps.edu
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