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(Random) (2.A) Coordinate and transformational geometry. 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;
(Random) (2.B) Coordinate and transformational geometry. 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;
(Random) (2.C) Coordinate and transformational geometry. Determine an equation of a line parallel or perpendicular to a given line that passes through a given point.
(Random) (3.B) Coordinate and transformational geometry. 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;
(Random) (3.C) Coordinate and transformational geometry. Identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane;
(Random) (4.B) Logical argument and constructions. 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;
(Random) (4.D) Logical argument and constructions. Compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.
(Random) (5.A) Logical argument and constructions. Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal
(Random) (5.A) Logical argument and constructions. Investigate patterns to make conjectures about geometric relationships, including criteria required for triangle congruence
(Random) (5.A) Logical argument and constructions. Investigate patterns to make conjectures about geometric relationships, including special segments of triangles
(Random) (5.A) Logical argument and constructions. Investigate patterns to make conjectures about geometric relationships, including diagonals of quadrilaterals
(Random) (5.A) Logical argument and constructions. Investigate patterns to make conjectures about geometric relationships, including interior and exterior angles of polygons
(Random) (5.A) Logical argument and constructions. Investigate patterns to make conjectures about geometric relationships, including special segments and angles of circles choosing from a variety of tools;
(Random) (5.B) Logical argument and constructions. Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge;
(Random) (5.C) Logical argument and constructions. Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships;
(Random) (6.A) Proof and congruence. 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;
(Random) (6.B) Proof and congruence. 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;
(Random) (6.C) Proof and congruence. Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles;
(Random) (6.D) Proof and congruence. 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;
(Random) (6.E) Proof and congruence. Prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems.
(Random) (7.A) Similarity, proof, and trigonometry. Apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles;
(Random) (7.B) Similarity, proof, and trigonometry. Apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems.
(Random) (8.A) Similarity, proof, and trigonometry. Prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems;
(Random) (8.B) Similarity, proof, and trigonometry. 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.
(Random) (9.A) Similarity, proof, and trigonometry. 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;
(Random) (9.B) Similarity, proof, and trigonometry. Apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.
(Random) (10.A) Two-dimensional and three-dimensional figures. 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;
(Random) (10.B) Two-dimensional and three-dimensional figures. 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.
(Random) (11.A) Two-dimensional and three-dimensional figures. Apply the formula for the area of regular polygons to solve problems using appropriate units of measure;
(Random) (11.B) Two-dimensional and three-dimensional figures. 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;
(Random) (11.C) Two-dimensional and three-dimensional figures. 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;
(Random) (11.D) Two-dimensional and three-dimensional figures. 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.
(Random) (12.A) Circles. Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems;
(Random) (12.B) Circles. Apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems;
(Random) (12.C) Circles. 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;
(Random) (12.D) Circles. 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;
(Random) (12.E) Circles. 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}.
(Random) (13.C) Probability. Identify whether two events are independent and compute the probability of the two events occurring together with or without replacement;