Using coordinates to prove properties of figures, and describing and composing rigid and non-rigid transformations.
G.2 Coordinate and transformational geometry: linking algebra and geometry and using one- and two-dimensional coordinates to test geometric conjectures
G.2A Locate the point lying a fractional part (under one) of the way along a segment in one or two dimensions, including the midpoint
G.2B Derive the midpoint, slope, and distance formulas and use them to verify congruent segments and parallel or perpendicular lines
G.2C Given a line and a point, write the equation of a line through the point that is parallel or perpendicular to it
G.3 Coordinate and transformational geometry: creating and describing rigid transformations (translation, reflection, rotation), dilations that keep similarity, and reductions or enlargements that do not
G.3A Describe and carry out transformations of plane figures using coordinate notation
G.3B Given a 2D figure, find its image or pre-image under compositions of rigid, non-rigid, or both kinds of transformations, including dilations centered anywhere in the plane
G.3C Give the sequence of transformations taking a pre-image to its image, whether or not a coordinate plane is used
G.3D Identify and tell apart reflectional and rotational symmetry in plane figures
Logical Argument and Constructions
Conditional statements, conjectures, and constructions with a compass and straightedge.
G.4 Logical argument and constructions: reasoning deductively to make sense of how geometric figures relate
G.4A Distinguish theorems, conjectures, postulates, definitions, and undefined terms from one another
G.4B Identify converse, inverse, and contrapositive of conditional statements and judge their truth, and link biconditionals to true conditionals with true converses
G.4C Show a conjecture is false by finding a counterexample
G.4D Compare Euclidean and spherical geometry, including parallel lines and triangle angle sums
G.5 Logical argument and constructions: using constructions to check conjectures about geometric figures
G.5A Conjecture from patterns, using tools, about transversal angles, triangle congruence criteria, special triangle segments, quadrilateral diagonals, polygon angles, and circle segments and angles
G.5B Use a compass and straightedge to construct congruent segments and angles, segment and angle bisectors, perpendicular lines, perpendicular bisectors, and a parallel line through an outside point
G.5C Make conjectures about geometric relationships from constructing perpendicular bisectors, angle bisectors, and congruent segments and angles
G.5D Use constructions to confirm the Triangle Inequality theorem and use it to solve problems
Proof and Congruence
Proving theorems about lines, angles and triangles, and proving triangles congruent.
G.6 Proof and congruence: proving and applying theorems through coordinate, transformational, or axiomatic approaches, written as flow charts, paragraphs, or two-column proofs
G.6A Verify theorems on angles from crossing lines (vertical angles, parallel lines with a transversal), prove perpendicular bisector points are equidistant from the endpoints, and solve problems
G.6B Prove triangles congruent using SAS, ASA, SSS, AAS, and Hypotenuse-Leg
G.6C Use the rigid-transformation definition of congruence to identify congruent figures and matching sides and angles
G.6D Verify triangle theorems, including a proof of the Pythagorean Theorem, interior angle sum, isosceles base angles, midsegments, and medians, and use them to solve problems
G.6E Prove a quadrilateral is a rectangle, square, rhombus, or parallelogram from its opposite sides, its opposite angles, or its diagonals, then solve problems
Similarity, Proof, and Trigonometry
Similar figures, the Pythagorean theorem, special right triangles and trigonometric ratios.
G.7 Similarity, proof, and trigonometry: applying similarity to solve problems
G.7A Use the dilation definition of similarity to identify similar figures, their proportional sides, and their congruent matching angles
G.7B Verify similar triangles with the Angle-Angle criterion, then use proportional corresponding sides to solve problems
G.8 Similarity, proof, and trigonometry: proving and applying theorems through coordinate, transformational, or axiomatic approaches, written as flow charts, paragraphs, or two-column proofs
G.8A Prove theorems about similar triangles, among them the Triangle Proportionality theorem, and use them to solve problems
G.8B Use the relationships created by drawing an altitude to a right triangle's hypotenuse, including geometric mean, to solve problems
G.9 Similarity, proof, and trigonometry: understanding and applying relationships in right triangles
G.9A Find side lengths and angle measures in right triangles using sine, cosine, and tangent
G.9B Solve problems with Pythagorean triples, the Pythagorean theorem, and the relationships in 45-45-90 and 30-60-90 special right triangles
Two- and Three-Dimensional Figures
Cross sections, nets, and area, surface area and volume of figures and solids.
G.10 Two- and three-dimensional figures: recognizing traits of 2D and 3D figures and how changing dimensions affects them
G.10A Identify 2D cross-sections of spheres, cones, cylinders, pyramids, and prisms, and the 3D objects formed by rotating 2D shapes
G.10B Describe how changing a shape's linear dimensions, proportionally or not, affects its volume, surface area, area, or perimeter
G.11 Two- and three-dimensional figures: applying formulas to find measures of 2D and 3D figures
G.11A Use the area formula for regular polygons to solve problems with proper units
G.11B Find the area of composite 2D figures made from sectors of circles, regular polygons, kites, trapezoids, parallelograms, or triangles, using appropriate units
G.11C Use total and lateral surface area formulas for spheres, cylinders, cones, pyramids, prisms, and composite solids to solve problems with proper units
G.11D Use volume formulas for spheres, cylinders, cones, pyramids, prisms, and composite solids to solve problems with proper units
Circles and Angles
Arc length, sector area, angles and segments in circles, and the equation of a circle.
G.12 Circles: understanding geometric relationships and applying theorems and equations about circles
G.12A Use circle theorems about secants, tangents, chords, radii, and angles to solve problems with no real-world context
G.12B Use the proportion between arc length and circumference to solve problems
G.12C Use the proportion between sector area and circle area to solve problems
G.12D Describe radian measure as the arc length intercepted by a central angle divided by the circle's radius
G.12E Show that x² + y² = r² describes a circle at the origin with radius r, and write (x − h)² + (y − k)² = r² for a circle with center (h, k)
Probability and Counting
Counting methods, probability of simple and compound events, and conditional probability.
G.13 Probability: understanding probability in real situations and applying independent and dependent events
G.13A Develop strategies for using permutations and combinations in real-world problems
G.13B Find probabilities from areas in real-world problems
G.13C Check if a pair of events is independent and find the probability that both happen, with or without replacement
G.13D Apply conditional probability to real-world problems
G.13E Apply independence to real-world problems
Mathematical Process Standards
The ways students do math at every grade: problem solving, choosing tools, communicating and justifying reasoning.
G.1 Mathematical process standards: using math processes to build and show understanding
G.1A Use math to solve problems from daily life, society, and work
G.1B Solve problems with a model of analyzing information, planning, finding and justifying a solution, then reviewing the process and whether the answer makes sense
G.1C Choose suitable tools (objects, manipulatives, paper, technology) and techniques (mental math, estimation, number sense) for solving problems
G.1D Explain mathematical ideas, reasoning, and consequences through symbols, diagrams, graphs, and words
G.1E Make representations, then use them to organize, record, and share mathematical ideas
G.1F Analyze mathematical relationships to link ideas and explain them
G.1G Show, explain, and defend mathematical ideas and arguments in speech or writing with exact mathematical vocabulary
There are 49 TEKS Geometry Standards on this page, in 8 strands: Coordinate and Transformational Geometry, Logical Argument and Constructions, Proof and Congruence, Similarity, Proof, and Trigonometry, Two- and Three-Dimensional Figures, Circles and Angles, Probability and Counting, and Mathematical Process Standards.
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What does a code like G.2A mean?
TEKS course codes read course, knowledge and skills statement, student expectation. In G.2A, the letter before the period names the course (A is Algebra I, G is Geometry), the number is the knowledge and skills statement, and the final letter is the student expectation under it.