GEOMETRY, PART 1

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.