# GEOMETRY, PART 1

## Price: $125 | Credits: One Semester | Dept: Math | Course ID# 223-1

This course is the first semester of Geometry and includes an introduction to the basics of Geometry, reasoning and proofs, perpendicular and parallel lines, congruent triangles, the anatomy of triangles, and similarity. This course is typically taken in the sequence with Geometry (Part 2) or is taken to replace credit for the first semester of Geometry. Geometry is approved by the University of California A-G as mathematics (category C).

Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course in an accelerated rate.

### LEARNING OBJECTIVES

In this module, students gain a comprehension of the following:

- To comprehend and identify the basic principles behind geometry, including the point, plane, line, and ray.
- How to classify polygons and angle pair relationships.
- To use the basics of reasoning and proof, including inductive and deductive reasoning, as well as conditional statement to prove angles and polygons similar and congruent.
- How to identify parallel vs. perpendicular lines as well as how to write equations of parallel and perpendicular lines.
- How to prove polygons congruent, using the SSS, SAS, ASA, and HL.
- To understand the concept of how corresponding parts of congruent triangles are congruent (CPCTC.)
- To identify and analyze isosceles and equilateral triangles.
- To find and use the points of concurrenty to make calculations, including the midsegments, perpendicular bisectors, angle bisectors, medians, and altitudes.
- Solving and proving similar triangles, including using ratios and proportions, as well as the geometric mean.

### TOPICS COVERED

- This course covers the following topics:
- Points, Lines, & Planes
- Measuring Segments
- Measuring & Classifying Angles
- Angle Pair Relationships
- Classifying Polygons
- Inductive Reasoning
- Deductive Reasoning
- Conditional Statements
- Proving Angles Congruent
- Parallel Lines With Transversals
- Proving Lines Parallel
- Parallel vs. Perpindicular Using Slope
- Write Equations of Lines
- Congruent Figures
- Congruent Triangles by SSS & SAS
- Congruent Triangles by AAS, ASA, & HL
- Isosceles and Equilateral Triangles
- Corresponding Parts of Congruent Triangles
- Midsegments of Triangles
- Perpindicular Bisectors of Triangles
- Angle Bisectors of Triangles
- Medians & Altitudes
- Inequalities in One Triangle
- Inequalities in Two Triangles
- Ratios & Proportions
- The Geometric Mean
- Similar Polygons
- Prove Triangles Similar by AA
- Prove Triangles Similar by SSS & SAS
- Similarity in Right Triangles