Math Department

High School Resources

High School Math Performance Standards

Geometry

Each ASD mathematics course reflects the program statement and incorporates the general program goals. In addition, each course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what a student should be able to do after successfully completing the course. After satisfactorily completing the ASD Geometry curriculum, a student will be proficient in the nine strands of mathematics which comprise the Geometry Math Content Standards. As evidence of proficiency, the student will be able to:

G:1 Number Sense

.1 Validate numerical solutions for application problems.
.2 Describe the number "Pi" and its relationship to a circle.
.3 Determine the circumference and area of circles and the surface area and volume of cylinders and spheres.
.4 Sketch diagrams that represent given information about measures of segments and angles.
.5 Explain restrictions on variables representing angles and lengths.

G:2 Computation

.1 Simplify expressions involving radicals and exponents.
.2 Simplify complex fractions.
.3 Evaluate formulas relevant to geometry including distance, midpoint, area, perimeter, volume, Pythagorean theorem, and quadratic formula.
.4 Set up and solve proportions involving similar figures.
.5 Compute measures of unknown parts of a right triangle using the sine, cosine, and tangent ratios.

G:3 Measurement

.1 Model and measure basic geometric figures using a variety of methods including paper folding, compass, straight edge, protractor, and technology.
.2 Use compass and straight edge for basic constructions.
.3 Use appropriate units to label solutions of application problems.

G:4 Theory

.1 Communicate both orally and in writing, using correct geometric vocabulary and notation.
.2 Explain the difference among definitions, postulates/axioms, and theorems.
.3 Explain the importance of the Parallel Postulate in Euclidean geometry.
.4 Classify problems as classical Euclidean geometry, coordinate geometry, or transformational geometry.
.5 Explain the difference between inductive and deductive reasoning.

G:5 Deduction

.1 State the converse, inverse and contrapositive of a conditional statement and determine the validity of each.
.2 Rewrite an "if and only if" statement into two conditional statements and vice versa.
.3 Prove conjectures related to geometric figures using paragraph proofs, indirect proofs, two-column proofs, and coordinate geometry proofs.
.4 Prove triangles are congruent using SSS, SAS, ASA, AAS, and HL.
.5 Use definitions of terms related to triangles (i.e. altitude, median, angle bisector, isosceles, etc.) to deduce other properties of triangles.
.6 Develop and explain the properties of trapezoids, parallelograms, rectangles, rhombuses, kites, and squares using the definitions of the various quadrilaterals.
.7 Prove two triangles are similar and write a valid proportion showing the relationship between the corresponding sides.
.8 Prove conjectures related to angles, parallel lines, and planes.

G:6 Diagrams and Models

.1 Select appropriate theorems to prove or disprove conjectures related to geometric figures.
.2 Identify, classify, and draw two-dimensional and three-dimensional figures.
.3 Draw and label triangles illustrating the congruency relationships of SSS, SAS, ASA, AAS, and HL.
.4 Identify and label corresponding parts of overlapping triangles.
.5 Identify and label congruent non-coplanar triangles in a three-dimensional diagram.
.6 Draw and label similar figures showing the correct relationship between corresponding parts.
.7 Solve problems involving triangles, quadrilaterals, and other polygons using appropriate terminology and properties.
.8 Identify and label angles, segments, and lines as they relate to circles, and use the properties to solve problems.
.9 Explain the difference among alternate interior angles, alternate exterior angles, corresponding angles, supplementary angles, and vertical angles formed by two lines and a transversal.
.10 Model and explain parallel, perpendicular, skew, and oblique lines.
.11 Describe the relationships of planes in space.
.12 Find interior and exterior angle measures of regular polygons.
.13 Confirm the validity of conjectures or provide a counter example using appropriate technology.

G:7 Probability

.1 Construct a sample space and list all possible outcomes of a particular event.
.2 Use probability to solve problems presented as geometric models.

G:8 Patterns

.1 Solve problems using the inequality relationships between the sides and angles of a triangle.
.2 Identify and use patterns from right triangles, including 30°-60°-90°, 45°-45°-90°, and Pythagorean triples to solve application problems.
.3 Identify and describe patterns that emerge from two-dimensional and three-dimensional geometric figures and use the patterns to solve problems.
.4 Identify, explain, and transform geometric figures using reflections, rotations, and translations on geometric figures.

G:9 Algebra

.1 Write and solve equations that model geometric relationships.
.2 Simplify and solve equations that result from formulas.
.3 Solve application problems using the appropriate formula or relationships.