# Washingon State Teacher Certification: Mathematics (5-12)

## Standard 4: Geometry and Measure

Candidates prove and understand geometric theorems and transformations as they apply to congruence, similarity, lines, triangles, trigonometry, circles, and measurements. In addition, the following content should be included; the relationship between geometryc figures and the Cartesian coordinate system.

4.A:
Understand congruence in terms of rigid motions and prove geometric theorems
4.B:
Apply transformations and use similarity and congruence in mathematical situations
4.C:
Perform geometric constructions physically and/or with technology
4.D:
Define trigonometric ratios and solve problems involving right triangles and general triangles
4.E:
Derive the Pythagorean Theorem and apply it to problem solving situations
4.F:
Identify and describe relationships among angles, radii, and chords
4.G:
Derive formulas for arc lengths and areas of sectors of circles
4.H:
Translate between the geometric description and the equation for a conic section
4.I:
Use coordinates to prove geometric theorems algebraically
4.J:
Derive area, surface area, and volume formulas and use them to solve problems
4.K:
Solve real life and mathematical problems involving angle measures and/or polygons
4.L:
Visualize and describe two-dimensional figures and three-dimensional objects as well as the relationships among them
4.M:
Apply geometric concepts to model real world situations

The B.S. degree in Mathematics, with a concentration in Secondary Education, covers these standards in the courses indicated in the table below.

 4.A 4.B 4.C 4.D 4.E 4.F 4.G 4.H 4.I 4.J 4.K 4.L 4.M Precalculus Mathematics I (MATH 121)† 1 1 Precalculus Mathematics II (MATH 122)† 1 3 1 1 1 1 2 2 Calculus Life Sciences I (MATH 131), orCalculus I (MATH 181) 2 2 2 3 Data Analysis (MATH 215) Discrete Mathematics (MATH 250) Calculus II (MATH 281) 2 2 2 2 2 3 Calculus III (MATH 282) 2 2 2 3 2 2 3 3 Calculus IV (MATH 283) 2 3 3 2 2 3 Introduction to Linear Algebra (MATH 289) 1 1 1 1 Differential Equations (MATH 312) 2 3 3 Probability and Statistics (MATH 315) Survey of Geometries (MATH 321) 3 3 3 2 3 3 3 3 2 Junior Seminar I (MATH 396) Junior Seminar II (MATH 397) Real Analysis I (MATH 451) 1 Abstract Algebra I (MATH 461) Senior Seminar I (MATH 496) Senior Seminar II (MATH 497) †While not required for the major, these classes are prerequisites for MATH 181