Download Arcadia Unified School District Geometry Grades 9

Arcadia Unified School District
Geometry
Grades 9-12
Introduction
The main purpose of the geometry curriculum is to
develop students' geometric skills and concepts and their
ability to construct formal logical arguments and proofs.
The skills and concepts in this discipline are useful to all
students. Throughout the course, students will
continually integrate previously learned algebraic skills in
geometric settings.
Geometry and Measurement
1. Students will demonstrate understanding by
identifying and giving examples of undefined terms,
postulates, theorems, definitions and properties.
Ρ Know how to add and subtract the measurement of
angles and segments
2. Students will write geometric proofs.
Spring 2009
1
Ρ Prove relationships between angles by using
properties of complementary, supplementary,
vertical, and exterior angles
Ρ Use indirect reasoning and indirect proof to reach a
conclusion
3. Students will demonstrate understanding of
inductive and deductive reasoning.
Ρ Construct and judge the validity of a logical
argument and give counterexamples to disprove a
statement
* Use inverse and contrapositive in logical arguments
4. Students will prove basic theorems involving
congruence and similarity.
Ρ Prove that triangles are congruent or similar
Ρ Use the concept of corresponding parts of congruent
and/or similar triangles
5. Students will know and be able to apply properties
of inequalities to triangles.
Ρ Recognize and use relationships between sides and
angles in a triangle
Ρ Apply the triangle inequality theorem
Spring 2009
2
Ρ Understand and write proofs with inequalities
involving two triangles
Spring 2009
3
6. Students will prove and use theorems involving the
properties of parallel lines cut by a transversal.
Ρ Prove lines are parallel from angle relationships
Ρ Apply slope to parallel and perpendicular lines
7. Students will prove and use theorems involving the
properties of quadrilaterals.
Ρ Use properties of parallelograms (including
rectangles, squares and rhombi) in proofs and in
solving problems
Ρ Apply trapezoid formulae
8. Students will prove and use theorems involving the
properties of circles.
Ρ Prove and solve problems regarding relationships
among arcs, chords, secants, tangents, inscribed
angles, and inscribed and circumscribed polygons of
circles
9. Students will know, derive, and solve problems
involving the perimeter, circumference, area,
volume, lateral area, and surface area of common
geometric figures.
Spring 2009
4
Ρ Find and use measures of sides, interior and exterior
angles of polygons (including regular polygons) to
classify figures and solve problems
Ρ Compute areas of polygons, including rectangles,
scalene triangles, equilateral triangles, rhombi,
parallelograms, and trapezoids
Ρ Compute the volumes and surface areas of prisms,
pyramids, cylinders, cones, and spheres, committing
to memory the applicable formulae
Ρ Determine how changes in dimensions affect the
perimeter, area, and volume of common geometric
figures and solids
* Utilize area formulae in computing geometric
probability
10. Students will prove and use the Pythagorean
theorem to find missing lengths of sides of right
triangles.
Ρ Know and are able to use angle and side relationships
in problems with special right triangles, such as 30o,
60o, 90o triangles and 45o, 45o, 90o triangles
Ρ Know and are able to use the first four Pythagorean
Triples
11. Students will perform basic constructions with
straightedge and compass.
Spring 2009
5
Ρ Construct an angle bisector
Ρ Construct a perpendicular bisector
Ρ Construct the line parallel to a given line through a
point off the line
Spring 2009
6
12. Students will demonstrate facility in using
coordinate geometry.
Ρ Graph linear equations using intercepts and
point/slope methods
Ρ Write linear equations with graphical information
given
Ρ Prove theorems by using coordinate geometry,
including midpoint of a line segment, distance
formula, and slope of a line
* Perform operations with vectors, including
magnitude and direction
* Use distance and midpoint formulae to locate points
in space
* Sketch and describe the locus of a given set of
conditions, as well as the intersection of loci
13. Students will know and understand the basic
trigonometric functions defined by the angles of a
right triangle.
Ρ Use trigonometric functions to solve for an unknown
length of a side draw unknown measure of an angle
* Know and are able to use elementary trigonometric
identities, i.e., tan x = (sinx/cosx), (sin x) 2 + (cos x)
2=1
Ρ Are able to solve a triangle using either the law of
sines or law of cosines
Spring 2009
7
14. Students will know and understand the effect of
mapping on figures in the coordinate plane and in
space.
*
*
Identify rotations, translations, and reflections
Transform figures using reflection, rotation,
translation and/or dilation
Spring 2009
8