Geometry
Develop spatial reasoning, logical proof, and the mathematical study of shape, size, and position, from foundational postulates to 3D solids and introductory trigonometry.
10 units and 57 lessons, for Grade 9 to Grade 10. Free on Slate.
Unit 1: Foundations of Geometry
Establish the axiomatic structure of geometry: undefined terms, definitions, postulates, and formal proof.
- Points, Lines, and Planes (10 min)
- Measuring Segments and Angles (10 min)
- Angle Relationships (10 min)
- Introduction to Proofs and Logical Reasoning (10 min)
- Conditional Statements and Logic (10 min)
- Midpoint and Distance in the Coordinate Plane (10 min)
Unit 2: Parallel and Perpendicular Lines
Explore the rich angle relationships that arise when lines are cut by a transversal.
- Parallel Lines Cut by a Transversal (10 min)
- Proving Lines Parallel (10 min)
- Perpendicular Lines and Their Properties (10 min)
- Slopes of Parallel and Perpendicular Lines (10 min)
Unit 3: Triangles and Congruence
Prove triangles congruent and use congruence to derive properties of geometric figures.
Unit 4: Triangle Relationships
Explore the rich geometry inside triangles through special segments and centers.
- Medians, Altitudes, and Angle Bisectors (10 min)
- The Four Triangle Centers (10 min)
- Triangle Inequality Theorem (10 min)
- Indirect Proof (Proof by Contradiction) (10 min)
- Similar Triangles: AA, SSS, SAS Similarity (10 min)
- Proportionality Theorems (10 min)
Unit 5: Right Triangles and Trigonometry
Master the Pythagorean theorem and introduce the trigonometric ratios that connect angle and side.
- The Pythagorean Theorem and Its Converse (10 min)
- Special Right Triangles: 45-45-90 and 30-60-90 (10 min)
- Trigonometric Ratios: Sine, Cosine, Tangent (10 min)
- Solving Right Triangles (10 min)
- Angles of Elevation and Depression (10 min)
- Law of Sines (10 min)
- Law of Cosines (10 min)
Unit 6: Quadrilaterals and Polygons
Classify and prove properties of quadrilaterals using congruence and parallel line theorems.
- Polygon Angle-Sum Theorems (10 min)
- Properties of Parallelograms (10 min)
- Rectangles, Rhombuses, and Squares (10 min)
- Trapezoids and Kites (10 min)
Unit 7: Transformations
Understand geometric transformations as functions on the plane that preserve or alter shape and size.
- Translations (10 min)
- Reflections (10 min)
- Rotations (10 min)
- Compositions of Transformations (10 min)
- Symmetry: Line and Rotational (10 min)
- Dilations and Scale Factor (10 min)
- Congruence and Similarity via Transformations (10 min)
Unit 8: Circles
Explore the deep geometry of circles: arcs, chords, tangents, and equations.
- Parts of a Circle (10 min)
- Arcs and Central Angles (10 min)
- Inscribed Angles (10 min)
- Tangent Lines and Their Properties (10 min)
- Chord, Secant, and Tangent Angle Relationships (10 min)
- Arc Length and Sector Area (10 min)
- The Equation of a Circle (10 min)
Unit 9: Area and Volume
Calculate and compare measurements of two- and three-dimensional figures with precision.
- Area of Polygons (10 min)
- Surface Area of Prisms and Cylinders (10 min)
- Surface Area of Pyramids, Cones, and Spheres (10 min)
- Volume of Prisms and Cylinders (10 min)
- Volume of Pyramids, Cones, and Spheres (10 min)
- Cavalieri's Principle and Cross-Sections (10 min)
- Geometric Probability (10 min)
Unit 10: Coordinate Geometry
Use algebraic tools to prove geometric theorems precisely on the coordinate plane.
- Classifying Figures Using Coordinates (10 min)
- Partitioning a Segment (10 min)
- Coordinate Proofs (10 min)