Geometry

Geometry is a required course for the college bound student.It is a study of the following topics in Euclidean Space: geometric patterns and figures, parallels, triangles, quadrilaterals, polygons, circles, basic trigonometric functions, loci and transformations, measurement in a plane and in space. Emphasis is placed upon the integration of coordinate geometry and algebraic problem solving. Appropriate technology, from manipulatives to calculators and graphics software, should be used regularly for instruction and assessment.

Pre-requisite

• Apply geometric properties and relationships to solve problems.
• Use formulas to solve problems.
• Define and use linear expressions to model and solve problems.
• Operate with matrices to model and solve problems.
• Apply the Pythagorean Theorem to solve problems.

Textbook:Glencoe Geometry, Cummins, McGraw Hill, 2004
Recommended Calculator: Scientific Calculator (TI 30 or better) minimum requirement

COMPETENCY GOAL 1:  The learner will perform operations with real numbers to solve problems. Objectives:

• Use length, area, and volume of geometric figures to solve problems. 
• Calculate arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.
• Use the trigonometric ratios to model and solve problems involving right triangles.
• Use length, area, and volume to model and solve problems involving probability.

COMPETENCY GOAL 2:  The learner will use geometric and algebraic properties of figures to solve problems. Objectives:

• Apply properties of angles, triangles, polygons, Pythagorean theorem, special right triangle, and circles to solve problems.
• Calculate and modify literal equations when using standard formulas such as slope, distance, midpoint, surface area, volume, and equation of a line.
• Integrate the properties of absolute value, inequalities, linear equations, radicals, and proportion to congruent and similar geometric figures.

COMPETENCY GOAL 3:  The learner will use geometric and algebraic properties of figures to write proofs. Objectives:

• Use logic and deductive reasoning to draw conclusions and solve problems.
• Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.
• Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:
• Triangles.
• Quadrilaterals.
• Other polygons.
• Circles.
• Develop and apply properties of solids to solve problems.

COMPETENCY GOAL 4:  The learner will analyze geometric figures in the coordinate plane algebraically. Objectives:

• Solve systems of equations and relate it to intersecting lines. Calculate size and scale change (x, y) ---> (ax, ay).
• Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.
• Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to describe the transformation of polygons in the coordinate plane.
• Write an analytic geometric proof.

COMPETENCY GOAL 5:  The learner will apply appropriate techniques, tools, and formulas to determine measurement. Objectives:

• Analyze precision, accuracy, and approximate error in measurement situations.
• Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders.
• Apply informal concepts of successive approximation, upper and lower bounds, land limit in measurement situations.

Technology Learning Outcomes:
The student can

• Combine graphics to create a new graphic.
• Utilize a flow chart to display information.