The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.
1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
2.0 Students write geometric proofs, including
proofs by contradiction.
3.0 Students construct and judge the validity
of a logical argument and give counterexamples to disprove a statement.
4.0 Students prove basic theorems involving
congruence and similarity.
5.0 Students prove that triangles are congruent
or similar, and they are able to use the concept of corresponding
parts of congruent triangles.
6.0 Students know and are able to use the triangle
inequality theorem.
7.0 Students prove and use theorems involving
the properties of parallel lines cut by a transversal, the properties
of quadrilaterals, and the properties of circles.
8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
11.0 Students determine how changes in dimensions
affect the perimeter, area, and volume of common geometric figures
and solids.
12.0 Students find and use measures of sides
and of interior and exterior angles of triangles and polygons
to classify figures and solve problems.
13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
14.0 Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to
determine distance and find missing lengths of sides of right
triangles.
16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2 + (cos( x )) 2 = 1.
19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.