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Skills available for Texas Geometry standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.

2 The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures.

3 The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity).

  • A describe and perform transformations of figures in a plane using coordinate notation;

  • 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, including dilations where the center can be any point in the plane;

  • C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane; and

  • D identify and distinguish between reflectional and rotational symmetry in a plane figure.

4 The student uses the process skills with deductive reasoning to understand geometric relationships.

  • A distinguish between undefined terms, definitions, postulates, conjectures, and theorems;

  • 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;

  • C verify that a conjecture is false using a counterexample; and

  • D compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.

5 The student uses constructions to validate conjectures about geometric figures.

6 The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

7 The student uses the process skills in applying similarity to solve problems.

8 The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

  • A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems; and

  • 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.

9 The student uses the process skills to understand and apply relationships in right triangles.

10 The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures.

  • 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; and

  • 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.

11 The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures.

  • A apply the formula for the area of regular polygons to solve problems using appropriate units of measure;

  • 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;

  • 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; and

  • 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.

12 The student uses the process skills to understand geometric relationships and apply theorems and equations about circles.

  • A apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems;

  • B apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems;

  • C apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems;

  • 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; and

  • E show that the equation of a circle with center at the origin and radius r is x² + y² = r² and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)² + (y - k)² =r².

13 The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events.