BENICIA UNIFIED SCHOOL DISTRICT
MATH STANDARDS
Geometry
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As
part of an on-going class project, students will be developing tutorial
presentations, definitions, and sample problems to help you better understand
the standards you are expected to achieve. Click on the links as they appear...and
watch these standards come alive!
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This course is designed for students who have successfully completed
an Algebra I course. This course includes a deductive method of proof
to justify theorems and to tell whether conclusions are valid. It
includes an investigation of the properties of both two and three-dimensional
geometric shapes.
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LOGIC
STUDENTS WILL:
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Demonstrate an understanding of point, line, plane, ray, segment,
and other basic geometry terms.
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Demonstrate knowledge of inductive and deductive reasoning.
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Write geometric proofs in any of these various forms (two-column,
paragraph, key step, flow-chart, indirect and coordinate geometry).
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Judge the validity of an argument, including giving counter examples
to disprove a statement.
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Analyze conditionals based on the converse, inverse, and contrapositive.
ANGLES
STUDENTS WILL:
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Learn and prove relationships between angles using properties of
complementary, supplementary, vertical and exterior, and interior angles
of polygons.
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Learn properties of parallel lines, including alternate interior
angles, corresponding angles, same-side interior angles, which make lines
parallel.
TRIANGLES
STUDENTS WILL:
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Use measures of sides and angles of triangles to classify types of
triangles.
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Use the concept of corresponding parts of congruent triangles are
congruent.
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Use the Triangle Inequality Theorem.
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Understand the concept of similarity and use it to determine whether
triangles are similar or not.
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Understand and use the Pythagorean Theorem and its converse.
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Apply the concepts of "special" right triangles such
as 30:60:90 triangles and 45:45:90 triangles.
POLYGONS
STUDENTS WILL:
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Explore and apply the properties of special quadrilaterals, including
parallelograms,
rectangles, squares, rhombus, and trapezoids.
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Give the appropriate name of the polygon and tell if it is regular,
given the sides and/or angle measures of polygons.
AREA/PERIMETER/VOLUME
STUDENTS WILL:
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Know, derive, and solve problems involving perimeter, circumference,
area, volume, lateral area, and surface area of common 2 and 3-dimensional
geometric shapes, including quadrilaterals, triangles, polygons, prisms,
pyramids, cylinders, cones, and spheres.
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Determine how changes in dimension affect the perimeter, area and
volume of common geometric figures and solids.
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Use the concept of area to compute Geometric Probabilities.
CIRCLES
STUDENTS WILL:
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Prove and solve problems regarding relationships among chords, secants,
tangents, inscribed angles, and inscribed and circumscribed polygons of
circles.
TRIGONOMETRY
STUDENTS WILL:
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Know the definitions of the basic trigonometric functions defined
by the angles of right triangles (i.e., sine, cosine, and tangent).
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Use trigonometric functions to solve for an unknown length of a side
of a right triangle, given an angle and a length of a side.
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Know and are able to use elementary relationships between the basic
trigonometric functions (i.e., tan(x) = sin (x) ( cos(x);(sin(x))2
+ (cos(x))2 = 1).
CONSTRUCTIONS
STUDENTS WILL:
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Perform basic constructions with straightledge and compass, such
as angle bisectors, perpendicular bisectors,
and the line parallel to a given line through a point off the line.
TRANSFORMATIONAL GEOMETRY
STUDENTS WILL:
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Know the effect of rigid motions on figures in the coordinate plane
and space, including rotations, translations, and reflections.
COORDINATE GEOMETRY
STUDENTS WILL:
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Prove theorems using coordinate geometry, including the midpoint
of a line segment, distance formula, and various forms of equations of
lines and circles.