Curriculum Map

Geometry

Develop spatial reasoning and logical proof. Congruence, similarity, circles, coordinate geometry, area, volume, and right-triangle trigonometry — with GeoGebra constructions and Desmos coordinate explorations. TEKS §111.41 aligned.

14 Units

Early Units (Foundation)

Building Skills

Advanced Concepts

Capstone/Synthesis

Foundations of Geometry

Explore the building blocks of geometry — points, lines, planes, segments, rays, and angles — and learn to classify angle pairs and perform basic constructions.

3-4 days

Logic and Proof

Learn the structure of conditional statements, develop deductive reasoning skills, and write your first geometric proofs in two-column and paragraph formats.

3-4 days

Parallel and Perpendicular Lines

Investigate the angle relationships created by transversals cutting parallel lines, prove lines are parallel using angle criteria, and connect parallelism to slope on the coordinate plane.

3-4 days

Triangle Congruence

Master the five triangle congruence criteria — SSS, SAS, ASA, AAS, and HL — and learn to write congruence proofs using CPCTC to establish that corresponding parts are equal.

3-4 days

Triangle Properties and Relationships

Investigate the special segments within triangles — midsegments, perpendicular bisectors, angle bisectors, medians, and altitudes — and apply the Triangle Inequality Theorem.

3-4 days

Similarity

Explore ratios, proportions, and the three triangle similarity criteria — AA, SAS, and SSS — and apply similar triangles to indirect measurement and real-world problem solving.

3-4 days

Quadrilaterals and Polygons

Classify and analyze quadrilaterals — parallelograms, rectangles, rhombuses, squares, and trapezoids — and extend your understanding to polygon angle sums and coordinate geometry proofs.

3-4 days

Circles

Explore the geometry of circles — central and inscribed angles, arc length, sector area, tangent lines, secants, and chord relationships — building a complete toolkit for circular reasoning.

4-5 days

Area and Perimeter

Derive and apply area formulas for triangles, quadrilaterals, and regular polygons, then combine them to find the area and perimeter of composite figures and analyze the effects of changing dimensions.

4-5 days

Surface Area and Volume

Calculate surface area and volume for prisms, cylinders, pyramids, cones, and spheres, then apply Cavalieri's principle and analyze composite solids and the effects of dimension changes.

4-5 days

Coordinate Geometry

Apply the distance formula, midpoint formula, and segment partitioning on the coordinate plane, derive the equation of a circle, and write coordinate proofs for geometric properties.

4-5 days

Transformations

Perform translations, reflections, rotations, and dilations on the coordinate plane, compose transformations, identify symmetry, and classify transformations as rigid or non-rigid.

4-5 days

Right Triangle Trigonometry

Define sine, cosine, and tangent ratios for right triangles, solve triangles using trigonometry, apply angles of elevation and depression, and explore special right triangles.

4-5 days

Geometry Capstone

Integrate the full geometry toolkit — proof, measurement, coordinate methods, transformations, and trigonometry — through geometric probability, multi-step modeling problems, and review of proof techniques.

4-5 days

Learning Progression

This course is designed to be taken sequentially. Earlier units establish foundational concepts that later units build upon. While you can explore units in any order, following the numbered sequence provides the most coherent learning experience.