The
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.

**MAJOR CONCEPTS**
**MAINTENANCE CONCEPTS
**

Logical
Reasoning
Ratios, Proportions

Properties
Perimeter, Area, Surface Area, Volume

Coordinate
Geometry
Equations

Angles
and Triangles
Formulas

**Standard I:****
**
**Logical Reasoning – The student will use deductive and inductive
reasoning to solve problems.
**

1.
Properties
and Relationships of Figures

a.
Identify
the relationships of parallel lines with a transversal.

b.
Identify
relationships between pairs of angles (e.g., adjacent, complementary,
vertical).

2.
Determine
and use the relationships of congruency and similarity to determine, unknown
values.

3.
Use logical
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.

**Standard 2:
****Properties of 2- and 3-Dimensional Figures – The student will use the properties and formulas of geometric figures to solve problems.
**

1.
Polygons

a.
Identify
and describe polygons (i.e., convex, concave, regular)

b.
Apply the
interior and exterior angle sum of convex polygons to solve problems.

c.
Develop and
apply the properties of quadrilaterals to solve problem (e.g., rectangles,
parallelograms, rhombi, trapezoids, kites).

2.
Draw and
analyze 2- and 3-dimensional figures.

3.
Use
properties of 2- and 3-dimensional figures to determine unknown values (e.g.,
given the perimeter/circumference, find the area).

4.
Compute
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.

5.
*Use
geometric tools (e.g., protractor, compass, straight edge) to construct a
variety of figures.

6.
Find angle
measures and arc measures related to circles.

7.
Chords,
Secants and Tangents

a.
Identify
and describe the relationship between two chords that intersect in the
interior of a circle.

b.
Identify
and describe the relationship between two secants that intersect in the
exterior of a circle.

c.
Identify
and describe the relationship between a secant and a tangent that intersect in
the exterior of a circle.

Standard
3:
Coordinate Geometry – The student will solve problems with geometric
figures in the coordinate plane.

1.
Use
transformations (reflections, rotation, translation) within coordinate
geometry (e.g., reflect points across the y-axis).

2.
Use
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.

3.
Given a set
of points determine the type of figure based on its properties (e.g.,
parallelogram, isosceles triangle, regular octagon).

Standard
4:
Angles, Triangles and Similar Polygons – The student will use the
properties of angles, right triangles and similar polygons to solve problems.

1.
Solve
problems using properties of angles (e.g., interior, exterior, complementary,
vertical, angle sums, 30-60-90).

2.
Use the
Pythagorean Theorem and its converse to find missing side lengths and to
determine acute, right, and obtuse triangles.

3.
Apply the
45-45-90 and 30-60-90 right triangle relationships to solve problems.

4.
Express the
trigonometric functions as ratios and derive the relationship between sine,
cosine, and tangent ratios, and use to solve real-world problems.

5.
Similar
Polygons

a.
Use similar
figures to construct ratios and solve for a missing side.

b.
Use ratios
of similar figures to find linear distance, perimeter, area, and volume.