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Geometry

Geometry is Everywhere. Geometry equations shown over city skyline.

Course Features

Course Duration: Full Year
Category: ,
Prerequisite: Algebra I
Assessment: Pre-Test, Lesson Practice, Unit Exams, Mid-Term Exam, Final Exam
Language: English

Course Details

Course Overview

The Acellus Geometry course offers a thorough exploration of geometric principles, equipping students with the skills to analyze shapes, spaces, and their properties in both two and three dimensions. Students will delve into foundational tools like points, lines, and planes, progressing to advanced topics such as congruence, similarity, trigonometry, transformations, and probability. Through interactive lessons, proofs, and real-world applications, learners will develop logical reasoning, problem-solving abilities, and the capacity to construct and interpret geometric figures. The course emphasizes precise measurements, coordinate geometry, and the relationships within and between shapes, fostering a deeper understanding of spatial reasoning.

By the end of the course, students will be proficient in calculating areas, volumes, and surface areas of various figures, proving geometric theorems, and applying trigonometric functions to solve problems. They will also explore conic sections, circles, and probability models, connecting geometry to broader mathematical concepts. This course prepares students for advanced mathematics, including precalculus and calculus, while highlighting geometry's relevance in fields like engineering, architecture, and physics.

Sample Lesson - Introduction to Geometry

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This course was developed by the International Academy of Science. Learn More

Scope and Sequence

Unit 1 – Tools of Geometry Students will learn the basics of geometric visualization using drawings, nets, and coordinate planes. They will identify and measure points, lines, segments, rays, and angles, applying postulates like the segment addition postulate. Lessons cover constructions, midpoints, distances, perimeters, and areas of basic shapes like squares, rectangles, triangles, and circles, including composite figures. Unit 2 – Reasoning and Proofs This unit introduces inductive and deductive reasoning, conditional statements, biconditionals, and properties of equality. Students will construct algebraic and geometric two-column proofs, using angle theorems to justify statements and validate mathematical propositions. Unit 3 – Parallel and Perpendicular Lines Students will explore transversals, parallel lines, and angle relationships, proving lines parallel or perpendicular. They will apply the angle sum theorem, construct parallel and perpendicular lines, and work with equations of lines, slopes, and spherical geometry comparisons. Unit 4 – Congruent Triangles This unit focuses on congruent figures and triangles, using postulates like SSS, SAS, ASA, AAS, and the hypotenuse-leg theorem. Students will solve for unknown measurements in isosceles, equilateral, and right triangles, and justify congruence in overlapping triangles. Unit 5 – Relationships within Triangles Students will study midsegments, perpendicular and angle bisectors, and triangle centers like circumcenter, incenter, centroid, and orthocenter. They will use indirect proofs and inequalities to analyze triangle sides, angles, and constructibility. Unit 6 – Polygons This unit covers polygon angle sums, properties of parallelograms, rhombuses, rectangles, squares, kites, and trapezoids. Students will prove special parallelograms, calculate midsegments and diagonals, and classify polygons using coordinates. Unit 7 – Similarity Students will solve proportions and identify similar polygons and triangles using theorems. They will apply the geometric mean, similarity in right triangles, and proportions from parallel lines, side-splitters, and angle bisectors. Unit 8 – Right Triangles and Trigonometry This unit introduces the Pythagorean theorem, special right triangles, and trigonometric ratios for solving sides and angles. Students will explore angles of elevation and depression, laws of sines and cosines, and real-world applications. Unit 9 – Transformations Students will perform translations, reflections, rotations, and compositions, identifying congruence and similarity transformations. They will also distinguish types of symmetry in figures. Unit 10 – Area This unit covers areas of parallelograms, rhombuses, kites, trapezoids, regular polygons, and similar figures. Students will use trigonometry for triangle areas, calculate arcs, sectors, composite shapes, and geometric probabilities. Unit 11 – Surface Area and Volume Students will calculate surface areas and volumes of prisms, cylinders, pyramids, cones, spheres, and composite figures. They will explore similar solids, cross sections, volumes of revolution, and applications like density and can design. Unit 12 – Circles This unit focuses on tangent lines, chords, arcs, inscribed angles, and segment lengths in circles. Students will work with loci, radian measures, conversions, and arc lengths. Unit 13 – Conic Sections Students will derive equations for parabolas, circles, ellipses, and hyperbolas, finding foci, directrices, and vertices. They will translate circles and partition line segments. Unit 14 – Probability This unit introduces experimental and theoretical probability, complements, relative frequency, and distributions. Students will use counting principles, permutations, combinations, compound probabilities, conditional probability, expected value, two-way tables, and identify independent versus dependent events. Following this unit students are presented with the Final Review and Exam.
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