Standard G-1:    The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

 

Indicators

G-1.1       Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries.

G-1.2       Communicate knowledge of geometric relationships by using mathematical terminology appropriately.

G-1.3       Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement.

G-1.4       Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software.

G-1.5       Use inductive reasoning to formulate conjectures.

G-1.6       Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement.

G-1.7       Understand the historical development of geometry.

G-1.8       Connect geometry with other branches of mathematics.

G-1.9       Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture, construction, farming, and astronomy).

G-1.10     Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing device)

 

Standard G-2:     The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

 

Indicators

G-2.1    Infer missing elements of visual or numerical geometric patterns (including triangular and rectangular numbers and the number of diagonals in polygons).

G-2.2    Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

G-2.3    Use the congruence of line segments and angles to solve problems.

G-2.4    Use direct measurement to determine the length of a segment, degree of an angle, and distance from a point to a line.

G-2.5    Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

G-2.6    Use scale factors to solve problems involving scale drawings and models.

G-2.7  Use geometric probability to solve problems.

 

Standard G-3:     The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

 

Indicators

G-3.1     Carry out a procedure to compute the perimeter of a triangle.

G-3.2     Carry out a procedure to compute the area of a triangle.

G-3.3     Analyze how changes in dimensions affect the perimeter or area of triangles.

G-3.4     Apply properties of isosceles and equilateral triangles to solve problems.

G-3.5     Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

G-3.6     Apply the triangle sum theorem to solve problems.

G-3.7     Apply the triangle inequality theorem to solve problems.

G-3.8     Apply congruence and similarity relationships among triangles to solve problems.

G-3.9     Apply theorems to prove that triangles are either similar or congruent.

G-3.10   Use the Pythagorean theorem and its converse to solve problems.

G-3.11   Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

G-3.12   Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

Standard G-4:     The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

 

Indicators

G-4.1      Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

G-4.2      Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

G-4.3      Apply procedures to compute measures of interior and exterior angles of polygons.

G-4.4      Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

G-4.5      Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

G-4.6      Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

 

Standard G-5:          The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

 

Indicators

G-5.1    Carry out a procedure to compute the circumference of circles.

G-5.2    Carry out a procedure to compute the area of circles.

G-5.3    Analyze how a change in the radius affects the circumference or area of a circle.

G-5.4    Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

G-5.5    Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

G-5.6    Apply the properties of lines that intersect circles (including two secants, two tangents, and a secant and a tangent) to solve problems.

G-5.7    Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

 

  Standard G-6:          The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

 

Indicators

G-6.1    Use the distance formula to solve problems.

G-6.2    Use the midpoint formula to solve problems.

G-6.3    Apply transformations—translation, reflection, rotation, and dilation—to figures in the coordinate plane by using sketches and coordinates.

G-6.4    Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

G-6.5    Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

G-6.6    Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

G-6.7    Carry out a procedure to compute the magnitude of the resultant of two perpendicular vectors by using the Pythagorean theorem.

G-6.8    Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

 

Standard G-7:           The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

 

Indicators

G-7.1    Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

G-7.2    Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

G-7.3    Analyze how changes in dimensions affect the volume of objects (including cylinders, prisms, and spheres).

G-7.4    Apply congruence and similarity relationships among geometric objects to solve problems.

G-7.5    Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

G-7.6    Apply a procedure to draw an isometric view of a three-dimensional object.