Geometry Course Outline
Every unit and lesson in Geometry, with proof built into each unit, from reasoning and transformations to circles, area and volume. Unit 10 covers the honors-track conic sections.
Try the student practice samples in the first expanded unit below. The detailed notes will be discussed during the course, with worked examples, guided practice, and time for questions. Enroll to work through the remaining lessons with your tutor.
Explore the study guide1Unit 1: Foundations and ReasoningUndefined terms, measurement, coordinate formulas, logic and the first proofs.7 lessons + review
- 1.1MCQ Sample
Points, Lines and Planes
Use undefined terms, postulates and notation.
- 1.2FRQ Sample
Segments and Distance
Measure segments and use the Segment Addition Postulate.
- 1.3Enroll Now
Angles and Angle Pairs
Classify angles and use complementary, supplementary and vertical pairs.
- 1.4Enroll Now
Midpoint and Distance in the Coordinate Plane
Apply the midpoint and distance formulas.
- 1.5Enroll Now
Inductive Reasoning
Make and test conjectures from patterns.
- 1.6Enroll Now
Conditional Statements and Deductive Reasoning
Write converses, inverses and contrapositives and use logic laws.
- 1.7Enroll Now
Algebraic and Two-Column Proofs
Write the first two-column proofs.
- 1REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 1.
2Unit 2: Parallel and Perpendicular LinesAngle pairs formed by transversals, proving lines parallel and the triangle angle sum.5 lessons + review
- 2.1Enroll Now
Lines and Transversals
Name angle pairs formed by a transversal.
- 2.2Enroll Now
Proving Lines Parallel
Use converses to prove lines are parallel.
- 2.3Enroll Now
Perpendicular Lines
Prove and apply theorems about perpendicular lines.
- 2.4Enroll Now
Slopes of Parallel and Perpendicular Lines
Use slope to classify and write lines.
- 2.5Enroll Now
The Triangle Angle-Sum Theorem
Prove the angle-sum and exterior-angle theorems.
- 2REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 2.
3Unit 3: TransformationsRigid motions and dilations on and off the coordinate plane, and symmetry.6 lessons + review
- 3.1Enroll Now
Translations
Translate figures with vectors and coordinate rules.
- 3.2Enroll Now
Reflections
Reflect figures over lines, including y = x.
- 3.3Enroll Now
Rotations
Rotate figures about a point by given angles.
- 3.4Enroll Now
Compositions of Transformations
Combine transformations and find a single equivalent one.
- 3.5Enroll Now
Dilations
Enlarge and reduce figures by a scale factor.
- 3.6Enroll Now
Symmetry
Identify line and rotational symmetry.
- 3REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 3.
4Unit 4: Congruent TrianglesCongruence through rigid motions, the triangle congruence criteria and CPCTC proofs.5 lessons + review
- 4.1Enroll Now
Congruence and Rigid Motions
Define congruence through rigid motions.
- 4.2Enroll Now
SSS and SAS Congruence
Prove triangles congruent by SSS and SAS.
- 4.3Enroll Now
ASA, AAS and HL Congruence
Prove triangles congruent by ASA, AAS and HL.
- 4.4Enroll Now
Proofs with Corresponding Parts
Use CPCTC to prove parts congruent.
- 4.5Enroll Now
Isosceles and Equilateral Triangles
Apply the base angles theorem and its converse.
- 4REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 4.
5Unit 5: Relationships in TrianglesBisectors, medians, altitudes, midsegments and the triangle inequalities.4 lessons + review
- 5.1Enroll Now
Perpendicular and Angle Bisectors
Use bisector theorems; find circumcenters and incenters.
- 5.2Enroll Now
Medians and Altitudes
Locate centroids and orthocenters.
- 5.3Enroll Now
Midsegments
Apply the Triangle Midsegment Theorem.
- 5.4Enroll Now
Triangle Inequalities
Order sides and angles and test possible side lengths.
- 5REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 5.
6Unit 6: Quadrilaterals and PolygonsAngle sums of polygons and the properties and proofs of special quadrilaterals.6 lessons + review
- 6.1Enroll Now
Polygon Angle Sums
Find interior and exterior angle sums of polygons.
- 6.2Enroll Now
Properties of Parallelograms
Use side, angle and diagonal properties of parallelograms.
- 6.3Enroll Now
Proving a Quadrilateral Is a Parallelogram
Prove parallelograms with the five tests.
- 6.4Enroll Now
Rectangles, Rhombuses and Squares
Classify special parallelograms by their diagonals.
- 6.5Enroll Now
Trapezoids and Kites
Use properties of trapezoids, midsegments and kites.
- 6.6Enroll Now
Coordinate Proofs
Prove properties of figures with coordinates.
- 6REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 6.
7Unit 7: Similarity and Right TrianglesSimilarity criteria, proportionality theorems, the Pythagorean Theorem and right-triangle trig.7 lessons + review
- 7.1Enroll Now
Ratios and Proportions
Solve proportions and use geometric means.
- 7.2Enroll Now
Similar Polygons
Identify similar polygons and scale factors.
- 7.3Enroll Now
AA, SSS and SAS Similarity
Prove triangles similar.
- 7.4Enroll Now
Proportionality Theorems
Use the Side-Splitter and Angle Bisector theorems.
- 7.5Enroll Now
The Pythagorean Theorem and Its Converse
Find missing sides and classify triangles.
- 7.6Enroll Now
Special Right Triangles
Use 45-45-90 and 30-60-90 relationships.
- 7.7Enroll Now
Right-Triangle Trigonometry
Use sine, cosine and tangent to solve right triangles.
- 7REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 7.
8Unit 8: CirclesTangents, arcs, chords, inscribed angles, segment relationships and circle equations.6 lessons + review
- 8.1Enroll Now
Parts of a Circle and Tangents
Identify parts of a circle and use tangent properties.
- 8.2Enroll Now
Arcs and Chords
Measure arcs and use chord relationships.
- 8.3Enroll Now
Inscribed Angles
Use the Inscribed Angle Theorem and its corollaries.
- 8.4Enroll Now
Angle Relationships in Circles
Find angles formed by chords, secants and tangents.
- 8.5Enroll Now
Segment Relationships in Circles
Use segment products for chords, secants and tangents.
- 8.6Enroll Now
Equations of Circles
Write and graph circles in standard form.
- 8REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 8.
9Unit 9: Perimeter, Area and VolumeArea of plane figures, arc length and sectors, and surface area and volume of solids.8 lessons + review
- 9.1Enroll Now
Perimeter and Area of Polygons
Find perimeter and area of triangles and quadrilaterals.
- 9.2Enroll Now
Circumference, Arc Length and Sector Area
Compute circumference, arc length and sector area.
- 9.3Enroll Now
Area of Regular Polygons
Use apothems to find areas of regular polygons.
- 9.4Enroll Now
Surface Area of Prisms and Cylinders
Find lateral and total surface area.
- 9.5Enroll Now
Surface Area of Pyramids, Cones and Spheres
Find surface area using slant height.
- 9.6Enroll Now
Volume of Prisms and Cylinders
Apply Cavalieri's principle and volume formulas.
- 9.7Enroll Now
Volume of Pyramids, Cones and Spheres
Find volumes of pointed solids and spheres.
- 9.8Enroll Now
Cross Sections and Solids of Revolution
Describe cross sections and solids formed by rotation.
- 9REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 9.
10Unit 10: Conic SectionsHonorsCircles, parabolas, ellipses and hyperbolas from their geometric definitions (honors track).4 lessons + review
- 10.1Enroll Now
Circles as Conic Sections
Derive the circle equation and complete the square.
- 10.2Enroll Now
Parabolas
Use focus and directrix to write parabolas.
- 10.3Enroll Now
Ellipses
Find foci, vertices and axes of ellipses.
- 10.4Enroll Now
Hyperbolas
Find foci, vertices and asymptotes of hyperbolas.
- 10REnroll Now
Unit Review
Mixed practice and a unit-test-style free-response set covering every lesson in Unit 10.
Independently developed by Code Scholars Tutoring. Lesson order and pacing can be adapted to the student’s school syllabus.