Geometry “I Can” Statements
Objectives
G.3.1
Students can
I can identify geometric figures, such as points, lines, planes, segments, rays, and angles.
I can represent geometric situations pictorially and label them using symbolic notation.
I can distinguish between undefined and defined terms.
G.3.2
I can differentiate between inductive and deductive reasoning.
I can draw conclusions through inductive reasoning by identifying patterns.
I can draw conclusions through deductive reasoning by applying definitions, postulates, and theorems.
I can justify conclusions in real-world situations.
G.3.3
I can use the basic concepts of symbolic logic.
I can identify the hypothesis and conclusion of a conditional statement.
I can generate the converse, inverse and contrapositive of a conditional statement.
I can validate conclusions through a variety of methods including the use of Venn diagrams.
G.3.4
I can construct logical arguments through direct reasoning.
I can construct logical arguments through indirect reasoning.
I can validate conclusions using formal and informal methods.
G.3.5
I can construct formal and informal proofs by applying definitions, theorems, and postulates.
I can construct formal and informal proofs related to complementary angles.
I can construct formal and informal proofs related to supplementary angles.
I can construct formal and informal proofs related to vertical angles.
I can construct formal and informal proofs related to angles formed by perpendicular lines.
I can justify steps in formal and informal proofs.
G.3.6
I can compare and contrast relationships between angles formed by two lines cut by a transversal when the lines are
parallel and when they are not parallel.
I can apply the relationships of alternate interior, alternate exterior, corresponding, and same side interior angle pairs
to justify parallelism.
G.3.7
I can make conjectures about congruence relationships with an emphasis on triangles.
I can justify congruence relationships with an emphasis on triangles.
I can apply congruence postulates to solve for unknowns in problems.
Geometry “I Can” Statements
G.3.8
I can distinguish between convex and concave quadrilaterals.
I can identify properties of parallelograms, rectangles, rhombuses, squares, and trapezoids.
I can compare and contrast the properties of quadrilaterals.
G.3.9
I can identify a real-world situation that involves similarity in two or three dimensions.
I can formulate a question and develop a hypothesis for a real-world situation involving similarity.
I can develop a method to collect, organize, and analyze related data.
I can justify a method to collect, organize, and analyze related data.
I can implement a method to collect, organize, and analyze related data.
I can generalize the results of the project to draw a conclusion.
I can compare the hypothesis and the conclusion of the project.
I can explain and summarize the conclusions using predictive and analytic tools of algebra and geometry.
I can present the project numerically, analytically, graphically and verbally with and without technology.
G.3.10
I can determine the existence of a triangle (triangle inequality) based on angle and side relationships.
I can establish the relationship between the measures of the angles and the lengths of the sides of a triangle with and without
technology.
G.3.11
I can verify and justify the basis for the trigonometric ratios by applying properties of similar triangles.
I can apply the concepts of trigonometric ratios to find inaccessible heights and distances.
I can apply the properties of similar triangles to find unknown side lengths.
I can apply the properties of similar triangles to find unknown angle measures.
I can construct a physical model that illustrates the use of a scale drawing in a real-world situation.
G.3.12
I can apply the Pythagorean Theorem to solve real-world problems.
I can apply the converse of the Pythagorean Theorem to solve real-world problems.
I can derive the special right triangle relationships through application of the Pythagorean Theorem.
G.3.13
I can investigate angle measures formed by chords of a circle and draw conclusions.
I can investigate angle measures formed by tangents of a circle and draw conclusions.
I can investigate angle measures formed by secants of a circle and draw conclusions.
I can investigate the relationships between arcs and related chords, tangents, and secants of a circle.
I can draw conclusions about the relationships between arcs and related chords, tangents, and secants of a circle.
G.3.14
I can solve for the measures of the interior angles of a polygon.
I can solve for the measures of the exterior angles of a polygon.
I can solve for the lengths of sides of a polygon from given data.
I can apply the properties of regular polygons to find unknown measurements of sides or angles.
Geometry “I Can” Statements
G.3.15
I can develop properties of tessellating figures.
I can apply the properties of tessellating figures to create a tessellation.
G.3.16
I can derive formulas for area, perimeter, surface area, and volume by various methods including nets.
I can justify formulas for area, perimeter, surface area, and volume by various methods including nets.
I can apply formulas for area, perimeter, surface area, and volume to solve real-world problems.
G.3.17
I can apply the concepts of analytical geometry, such as formulas for distance, slope, and midpoint.
I can apply the concepts of analytical geometry to find dimensions of polygons on the coordinate plane.
G.3.18
I can construct the medians of a triangle using various methods.
I can construct the altitudes of a triangle using various methods.
I can construct the angle bisectors of a triangle using various methods.
I can construct the perpendicular bisectors of a triangle using various methods.
I can develop logical concepts about the relationships between medians, altitudes, angle bisectors and perpendicular
bisectors to be used in solving real-world problems.
G.3.19
I can create and apply concepts of a reflection using transformational geometry and laws of symmetry.
I can create and apply concepts of a translation using transformational geometry and laws of symmetry.
I can create and apply concepts of a rotation using transformational geometry and laws of symmetry.
I can create and apply concepts of a glide reflection using transformational geometry and laws of symmetry.
I can create and apply concepts of a dilation using transformational geometry and laws of symmetry.
I can develop logical arguments for congruency and similarity in transformational geometry.
G.3.20
I can compare and contrast Euclidean geometry to other geometries such as spherical or elliptic.
I can utilize various forms of communication such as physical models, oral and written reports to categorize geometries.
G.3.21
I can approximate the area of irregularly shaped regions based on the approximations and attributes of the related regions.
I can develop a formula to find the area of irregularly shaped regions.
I can justify a formula to find the area of irregularly shaped regions.
I can plan, organize and present the results of the related investigation.