following skills are required of all students completing Geometry.
Major Concepts should be taught in depth using a variety of
methods and applications (concrete to the abstract).
Maintenance Concepts have been taught previously and are a
necessary foundation for this course. The
major concepts are considered minimal exit skills and districts are strongly
encouraged to exceed these skills when building a Geometry curriculum.
Visual and physical models, calculators, and other technologies are
recommended when appropriate and can enhance both instruction and assessment.
Perimeter, Area, Surface Area, Volume
Logical Reasoning – The student will use deductive and inductive
reasoning to solve problems.
and Relationships of Figures
the relationships of parallel lines with a transversal.
relationships between pairs of angles (e.g., adjacent, complementary,
and use the relationships of congruency and similarity to determine, unknown
reasoning skills (inductive and deductive) to make and test conjectures,
formulate counter examples, follow logical arguments, judge the validity of
arguments and construct simple valid arguments.
Properties of 2- and 3-Dimensional Figures – The student will use the properties and formulas of geometric figures to solve problems.
and describe polygons (i.e., convex, concave, regular)
interior and exterior angle sum of convex polygons to solve problems.
apply the properties of quadrilaterals to solve problem (e.g., rectangles,
parallelograms, rhombi, trapezoids, kites).
analyze 2- and 3-dimensional figures.
properties of 2- and 3-dimensional figures to determine unknown values (e.g.,
given the perimeter/circumference, find the area).
length, perimeter or circumference, area, volume, and surface area of
geometric figures with missing information and correctly identify the
appropriate unit of measure of each.
geometric tools (e.g., protractor, compass, straight edge) to construct a
variety of figures.
measures and arc measures related to circles.
Secants and Tangents
and describe the relationship between two chords that intersect in the
interior of a circle.
and describe the relationship between two secants that intersect in the
exterior of a circle.
and describe the relationship between a secant and a tangent that intersect in
the exterior of a circle.
Coordinate Geometry – The student will solve problems with geometric
figures in the coordinate plane.
transformations (reflections, rotation, translation) within coordinate
geometry (e.g., reflect points across the y-axis).
coordinate geometry to find the distance between two points; the midpoint of a
segment; and to calculate the slopes of parallel, perpendicular, horizontal,
and vertical lines.
Given a set
of points determine the type of figure based on its properties (e.g.,
parallelogram, isosceles triangle, regular octagon).
Angles, Triangles and Similar Polygons – The student will use the
properties of angles, right triangles and similar polygons to solve problems.
problems using properties of angles (e.g., interior, exterior, complementary,
vertical, angle sums, 30-60-90).
Pythagorean Theorem and its converse to find missing side lengths and to
determine acute, right, and obtuse triangles.
45-45-90 and 30-60-90 right triangle relationships to solve problems.
trigonometric functions as ratios and derive the relationship between sine,
cosine, and tangent ratios, and use to solve real-world problems.
figures to construct ratios and solve for a missing side.
of similar figures to find linear distance, perimeter, area, and volume.