# 420 Geometry

2 semesters, 1 credit

Open to sophomores and juniors

Prerequisites: Minimum grade of C in 410 Algebra I and/or teacher approval

In Geometry, students will learn how geometric shapes relate to our world. They will develop logic and reasoning skills through writing two-column proofs. Students will study various topics such as congruent triangles, properties of parallel lines, polygons, similar triangles, Pythagorean theorem, right triangle trigonometry, transformations, and circles. A TI-84 graphing calculator is required for this class.

### Skills

By the completion of this course, students will be able to…

1. Correctly use the symbols, definitions, properties, postulates, and theorems of geometry in proofs and application problems.
2. Write proofs based on valid assumptions and deductive logic using definitions, properties, postulates, and theorems.
3. Apply the geometric concepts of congruence, similarity, parallelism, and equality to application problems.
4. Demonstrate their understanding of the attributes of polygons and solids by correctly calculating areas, perimeters, surface areas, and volumes.
5. Apply their knowledge of ratios to relationships among the parts of a triangle, specifically sine, cosine, and tangent.
6. Create geometric diagrams, including triangles, parallel lines cut by a transversal, polygons, and circles.
7. Find the sine, cosine, and tangent of an angle.

### Knowledge

By the completion of this course, students will know…

1. Basic defined and undefined terms such as distance, angles, congruent segments, congruent angles, types of triangles, conditional statements, postulates, and theorems
2. The purpose of a two column proof and how to write one
3. The principles of parallel lines and planes, perpendicular lines, skew lines, angles formed by two lines cut by a transversal, sum of angles in a triangle, exterior angle of triangle properties, types of polygons, and the sum of interior and exterior angles of polygons
4. The principles of congruent triangles, medians, triangle centers, altitudes, angle, and segment bisectors in triangles
5. The structure of parallelograms, rectangles, rhombuses, squares, trapezoids, and triangles
6. The purpose of ratios, proportions and similar polygons as well as applications involving similar triangles
7. Properties of right triangles, special right triangles, basic trigonometric ratios,  and applications involving angles of elevation and depression
8. Circle vocabulary and properties of angles and arcs in a circle

This course last updated on January 27, 2021, by the Math Department.