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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

40-55 minutes per unit

What You Will Learn

Proof & Reasoning

Build deductive arguments from axioms to theorems. Two-column, paragraph, and coordinate proofs.

Interactive Constructions

GeoGebra dynamic constructions and Desmos coordinate geometry — manipulate figures to discover properties.

TEKS §111.41 Aligned

Covers Texas Essential Knowledge and Skills for Geometry.

All Units

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.

•Identify and name points, lines, planes, segments, and rays using correct notation
•Measure and classify angles as acute, right, obtuse, or straight
•Identify and apply relationships between complementary, supplementary, and vertical angle pairs
+1 more objectives

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.

•Identify the hypothesis and conclusion of a conditional statement and write its converse, inverse, and contrapositive
•Distinguish between inductive and deductive reasoning and recognize valid logical arguments
•Apply the Laws of Detachment and Syllogism to draw logical conclusions
+1 more objectives

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.

•Identify corresponding, alternate interior, alternate exterior, and consecutive interior angles formed by a transversal
•Apply angle relationship theorems to find missing angle measures when parallel lines are cut by a transversal
•Prove that two lines are parallel using converse theorems about angle pairs
+1 more objectives

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.

•Identify corresponding parts of congruent triangles and write correct congruence statements
•Determine whether two triangles are congruent using SSS, SAS, ASA, AAS, or HL
•Write two-column proofs establishing triangle congruence
+1 more objectives

Triangle Properties and Relationships

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

•Apply the Triangle Midsegment Theorem to find lengths and establish parallelism
•Identify and apply properties of perpendicular bisectors, angle bisectors, medians, and altitudes
•Locate and describe the four triangle centers: circumcenter, incenter, centroid, and orthocenter
+1 more objectives

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.

•Solve proportions and apply properties of proportional relationships to geometric figures
•Determine whether two triangles are similar using AA, SAS, or SSS similarity criteria
•Apply the properties of similar triangles to find unknown side lengths and angle measures
+1 more objectives

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.

•Classify quadrilaterals by their properties and understand the hierarchy of special quadrilaterals
•Apply properties of parallelograms, rectangles, rhombuses, squares, and trapezoids to solve problems
•Calculate interior and exterior angle sums for convex polygons
+1 more objectives

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.

•Identify and name parts of a circle including radii, diameters, chords, secants, tangents, arcs, and sectors
•Apply the relationships between central angles, inscribed angles, and intercepted arcs
•Calculate arc length and sector area using proportional reasoning
+1 more objectives

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.

•Derive and apply area formulas for triangles, parallelograms, trapezoids, rhombuses, kites, and regular polygons
•Calculate the area and perimeter of composite figures by decomposing them into familiar shapes
•Predict how changes in linear dimensions affect area and perimeter

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.

•Calculate the surface area and volume of prisms, cylinders, pyramids, cones, and spheres
•Apply Cavalieri's principle to justify volume formulas for oblique solids
•Find the surface area and volume of composite solids
+1 more objectives

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.

•Apply the distance formula and midpoint formula to solve problems on the coordinate plane
•Partition a directed line segment in a given ratio
•Derive and apply the standard equation of a circle from the distance formula
+1 more objectives

Transformations

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

•Describe and perform translations, reflections, rotations, and dilations using coordinate rules
•Determine whether a transformation is rigid (isometry) or non-rigid
•Compose multiple transformations and describe the resulting mapping
+1 more objectives

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.

•Define and calculate the sine, cosine, and tangent ratios for acute angles in right triangles
•Use trigonometric ratios to find unknown side lengths and angle measures in right triangles
•Solve real-world problems involving angles of elevation and depression
+1 more objectives

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.

•Apply geometric probability using area and length models
•Synthesize proof techniques from across the course to construct multi-step arguments
•Solve real-world modeling problems that integrate measurement, coordinate geometry, and trigonometry
+1 more objectives

Geometry. Texas FHSP graduation requirement. TEKS §111.41 aligned. Prerequisite: Algebra I.