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Identify the basic objects and relations of geometry and measures angles and segments
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you identify points, lines, line segments and angles, and labels them appropriately
you measure segments with a ruler and angles with a protractor
you demonstrate understanding of congruence of segments and angles
you demonstrate skill in completing simple proofs
you show how to use the basic geometric constructions
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Solve problems involving triangles
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you identify the different types of triangles
you identify congruent triangles
you solve problems concerning angles by using the fact about the sum of the measures of the angles
you use the theorems on congruence (SSS, SAS, ASA, HL) to prove other theorems and solve problems
you analyze components of problems using the theorems and definitions to solve progressively more complex problems
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Use parallel lines and figures with parallel lines
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you identify parallel, corresponding angles, alternate interior angles, interior angles
you use the axioms and theorems concerning parallel lines
you identify quadrilaterals with parallel lines: trapezoid, parallelogram, rhombus, rectangle, square
you apply the various properties of such quadrilaterals to solving problems which combine one or more such figures
you demonstrate skill in constructions using parallel lines
you identify the role of Euclid's 5th Postulate in the evolution of modern mathematics
you recognize the impossibility of certain constructions
you apply the process for solving progressively more complex problems according to the problem solving criteria
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Solve problems using the Pythagorean Theorem and its converse
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you summarize the Pythagorean Theorem and its converse
you compute a missing side of a right triangle
you show that 3 given sides form a right triangle by using the converse of the Pythagorean Theorem
you construct Pythagorean Triples using any pair of generators and demonstrate understanding of the influence in the development of modern abstract mathematics culminating in Andrew Wiles proof of Fermat's Last Theorem in 1994
you apply skill to applied geometric problems
you apply the process for solving progressively more complex problems according to the problem solving criteria
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Compute perimeters and areas of geometric shapes
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you illustrate the importance of the assumption that congruent polygons have equal areas
you calculate the area of non-overlapping unit squares covering a figure
you distinguish rectangles, squares, parallelograms and triangles so that the appropriate formulas for perimeter and area can be used
you apply the correct formulas to models of the geometric objects
you apply the process for solving progressively more complex problems according to the problem solving criteria
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Solve problems involving similar triangles and other similar figures
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you describe the concept of similar figures and points out examples in scale drawings and maps
you identify when two triangles are similar using the AA fact
you solve for missing parts of pairs of similar triangles
you apply skill to dissecting and analyzing complex problems into component pairs of similar triangles
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Solve problems using right triangle trigonometry (optional)
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you summarize the definition of sin, cos, tan
you calculate the sin, cos, tan of any angle in degrees using a scientific calculator
you use sine, cosine, and tangent ratios to compute sides and/ or angles of right triangles
you solve for missing parts of right triangles which model real world problems
you apply the process for solving problems according to the problem solving criteria
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Solve problems involving circles
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you identify circles and the various parts: radius, diameter, chord, central angle
you use the definition of arc measure and the formula for the measure of an inscribed angle to solve for angles formed by radii, diameters and chords
you use the fact that a tangent line and the radius drawn to the point of tangency are perpendicular
you apply skill to applied problems modeled by circles and lines
you apply the process for solving progressively more complex problems according to the problem solving criteria
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Solve solid geometry problems involving solids in space
Assessment Strategies
by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
Criteria
you identify relationships between lines and planes in space
you distinguish the different solids (polyhedra, prisms, rectangular solids, pyramids, tetrahedra, cylinders, cones, and spheres
you calculate volumes and surface areas of the different solids usings appropriate formulas
you use the extension of the Pythagorean Theorem in space
you extend the facts of plane geometry to the parts of solid figures
you apply the process for solving progressively more complex problems according to the problem solving criteria