This course is the first semester of Geometry and includes an introduction to the basics of Geometry, measurements and proofs, parallel and perpendicular lines, rigid motion and congruence, relationships in 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 at an accelerated rate.
In this module, students gain a comprehension of the following:
• The foundations of geometry, including points, lines, planes, segments, angles, polygons, circles, and geometric constructions.
• Methods for measuring and classifying segments and angles, including the use of distance, midpoint, perimeter, circumference, and area formulas.
• Relationships between angles, including angle pairs formed by transversals intersecting parallel lines.
• The principles of inductive and deductive reasoning and how they are used to justify mathematical conclusions.
• The structure and interpretation of conditional statements, including converse, inverse, and contrapositive forms.
• The process of writing and justifying algebraic, segment, and angle proofs using logical reasoning.
• Techniques for identifying and proving relationships between parallel and perpendicular lines, including writing equations of - lines using slope and given points.
• Multiple forms of linear equations, including slope-intercept, point-slope, and standard form.
• The role of rigid transformations (translations, reflections, and rotations) in analyzing symmetry and congruence.
• The conditions required to prove figures and triangles congruent using SSS, SAS, ASA, AAS, HL, and CPCTC.
• The properties of special triangles, including isosceles and equilateral triangles.
• The relationships within triangles, including midsegments, perpendicular bisectors, angle bisectors, medians, and altitudes.
• The construction and properties of triangle centers, including the circumcenter, incenter, centroid, and orthocenter.
• The use of indirect proofs and the application of inequalities in one and two triangles.
• The concept of ratios, proportions, and scale factors in solving geometric problems.
• The conditions for similarity and methods for proving triangles similar using SSS, SAS, and AA similarity theorems.
• The application of dilations, geometric mean relationships, and proportional reasoning to solve problems involving similar figures and parallel lines.
