TexasTexas High School Geometry Curriculum
Video lessons and practice for every high school Geometry topic. Aligned to Texas TEKS standards so students can keep up with class or get ahead.
Texas High School Geometry Curriculum | StudyPugHelp
ID | Strand & Expectation | StudyPug Topic |
|---|---|---|
TX.G.2.A | Determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint |
TX.G.2.B | Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines |
TX.G.2.C | Determine an equation of a line parallel or perpendicular to a given line that passes through a given point |
TX.G.3.A | Describe and perform transformations of figures in a plane using coordinate notation |
TX.G.3.B | Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both |
TX.G.3.C | Identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane |
TX.G.3.D | Identify and distinguish between reflectional and rotational symmetry in a plane figure |
TX.G.4.A | Distinguish between undefined terms, definitions, postulates, conjectures, and theorems |
TX.G.4.B | Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse |
TX.G.4.D | Compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle |
TX.G.5.A | Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools |
TX.G.5.D | Verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems |
TX.G.6.A | Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems |
TX.G.6.B | Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions |
TX.G.6.D | Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems |
TX.G.6.E | Prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems |
TX.G.7.A | Apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles |
TX.G.8.B | Identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems |
TX.G.9.A | Determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems |
TX.G.9.B | Apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems |
TX.G.10.A | Identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes |
TX.G.10.B | Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change |
TX.G.11.B | Determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure |
TX.G.11.C | Apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure |
TX.G.11.D | Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure |
TX.G.12.A | Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems |
TX.G.12.B | Apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems |
TX.G.12.D | Describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle |
TX.G.12.E | Show that the equation of a circle with center at the origin and radius r is x^2 + y^2 = r^2 and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)^2 + (y - k)^2 = r^2 |
TX.G.13.A | Develop strategies to use permutations and combinations to solve contextual problems |
TX.G.13.B | Determine probabilities based on area to solve contextual problems |
TX.G.13.C | Identify whether two events are independent and compute the probability of the two events occurring together with or without replacement |
TX.G.13.D | Apply conditional probability in contextual problems |
TX.G.13.E | Apply independence in contextual problems |
Texas High School Geometry Topics
This course covers all 41 TEKS Geometry standards taught in Texas high schools. Topics are organized into clear chapters so students can find exactly what they need for homework or exam prep.
Coordinate Geometry
Students learn to find the midpoint and partition a segment at a given fractional distance, then use the distance, slope, and midpoint formulas to verify congruence, parallelism, and perpendicularity. They also determine equations of parallel and perpendicular lines through a given point.
Transformations and Symmetry
Texas Geometry students describe and perform transformations using coordinate notation, determine images and pre-images under compositions of rigid and non-rigid transformations, and identify sequences of transformations that map a pre-image onto an image. They also distinguish between reflectional and rotational symmetry.
Logical Reasoning and Proof
Students distinguish undefined terms, definitions, postulates, conjectures, and theorems. They analyze conditional statements — converse, inverse, and contrapositive — and connect biconditional statements to true conditionals. Counterexamples are used to disprove conjectures, and Euclidean geometry is compared to spherical geometry.
Geometric Relationships and Constructions
Using a compass and straightedge, students construct congruent segments and angles, bisectors, perpendicular lines, and parallel lines. Constructions are used to make conjectures about angles formed by parallel lines, triangle inequality, vertical angles, and perpendicular bisectors.
Triangle Congruence and Similarity
Students prove triangle congruence using SAS, ASA, SSS, AAS, and HL conditions. They apply the definition of congruence in terms of rigid transformations. For similarity, students apply AA criterion, Triangle Proportionality theorem, and geometric mean relationships from altitude-on-hypotenuse problems.
Right Triangles and Trigonometry
Students apply sine, cosine, and tangent ratios to find side lengths and angle measures. Special right triangles — 30-60-90 and 45-45-90 — and Pythagorean triples are used to solve real-world and mathematical problems.
Three-Dimensional Figures
Students identify cross-sections of prisms, pyramids, cylinders, cones, and spheres. They explore how changes in linear dimensions affect perimeter, area, surface area, and volume, then apply formulas for surface area and volume to composite three-dimensional figures.
Circles
Circle theorems cover angles, radii, chords, tangents, and secants. Students apply proportional relationships for arc length and sector area, describe radian measure, and derive the equation of a circle in standard form: (x – h)² + (y – k)² = r².
Probability
Students use permutations and combinations to solve problems, determine geometric probability using area models, identify independent events, compute probabilities with and without replacement, and apply conditional probability in contextual situations.