No records

912.G.SRT.2 
12 
Geometry 
Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. 


912.G.SRT.3 
9 
Geometry 
Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 


912.G.SRT.3 
10 
Geometry 
Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 


912.G.SRT.3 
11 
Geometry 
Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 


912.G.SRT.3 
12 
Geometry 
Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 


912.G.SRT.4 
9 
Geometry 
Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 


912.G.SRT.4 
10 
Geometry 
Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 


912.G.SRT.4 
11 
Geometry 
Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 


912.G.SRT.4 
12 
Geometry 
Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 


912.G.SRT.5 
9 
Geometry 
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 


912.G.SRT.5 
10 
Geometry 
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 


912.G.SRT.5 
11 
Geometry 
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 


912.G.SRT.5 
12 
Geometry 
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 


912.G.SRT.6 
9 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 


912.G.SRT.6 
10 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 


912.G.SRT.6 
11 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 


912.G.SRT.6 
12 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 


912.G.SRT.7 
9 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles. 


912.G.SRT.7 
10 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles. 


912.G.SRT.7 
11 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles. 


912.G.SRT.7 
12 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles. 


912.G.SRT.8 
9 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 


912.G.SRT.8 
10 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 


912.G.SRT.8 
11 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 


912.G.SRT.8 
12 
Geometry 
Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 


912.G.SRT.9 
9 
Geometry 
Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. 


912.G.SRT.9 
10 
Geometry 
Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. 


912.G.SRT.9 
11 
Geometry 
Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. 


912.G.SRT.9 
12 
Geometry 
Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. 


912.G.SRT.10 
9 
Geometry 
Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems. 


912.G.SRT.10 
10 
Geometry 
Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems. 


912.G.SRT.10 
11 
Geometry 
Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems. 


912.G.SRT.10 
12 
Geometry 
Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems. 


912.G.SRT.11 
9 
Geometry 
Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). 


912.G.SRT.11 
10 
Geometry 
Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). 


912.G.SRT.11 
11 
Geometry 
Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). 


912.G.SRT.11 
12 
Geometry 
Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). 


912.G.C.1 
9 
Geometry 
Understand and apply theorems about circles. Prove that all circles are similar. 


912.G.C.1 
10 
Geometry 
Understand and apply theorems about circles. Prove that all circles are similar. 


912.G.C.1 
11 
Geometry 
Understand and apply theorems about circles. Prove that all circles are similar. 


912.G.C.1 
12 
Geometry 
Understand and apply theorems about circles. Prove that all circles are similar. 


912.G.C.2 
9 
Geometry 
Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. 


912.G.C.2 
10 
Geometry 
Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. 


912.G.C.2 
11 
Geometry 
Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. 


912.G.C.2 
12 
Geometry 
Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. 


912.G.C.3 
9 
Geometry 
Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 


912.G.C.3 
10 
Geometry 
Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 


912.G.C.3 
11 
Geometry 
Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 


912.G.C.3 
12 
Geometry 
Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 


912.G.C.4 
9 
Geometry 
Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle. 


912.G.C.4 
10 
Geometry 
Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle. 


912.G.C.4 
11 
Geometry 
Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle. 


912.G.C.4 
12 
Geometry 
Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle. 


912.G.C.5 
9 
Geometry 
Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 


912.G.C.5 
10 
Geometry 
Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 


912.G.C.5 
11 
Geometry 
Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 


912.G.C.5 
12 
Geometry 
Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 


912.G.GPE.1 
9 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 


912.G.GPE.1 
10 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 


912.G.GPE.1 
11 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 


912.G.GPE.1 
12 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 


912.G.GPE.2 
9 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix. 


912.G.GPE.2 
10 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix. 


912.G.GPE.2 
11 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix. 


912.G.GPE.2 
12 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equation of a parabola given a focus and directrix. 


912.G.GPE.3 
9 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 


912.G.GPE.3 
10 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 


912.G.GPE.3 
11 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 


912.G.GPE.3 
12 
Geometry 
Translate between the geometric description and the equation for a conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 


912.G.GPE.4 
9 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2). 


912.G.GPE.4 
10 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2). 


912.G.GPE.4 
11 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2). 


912.G.GPE.4 
12 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2). 


912.G.GPE.5 
9 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 


912.G.GPE.5 
10 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 


912.G.GPE.5 
11 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 


912.G.GPE.5 
12 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 


912.G.GPE.6 
9 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 


912.G.GPE.6 
10 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 


912.G.GPE.6 
11 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 


912.G.GPE.6 
12 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 


912.G.GPE.7 
9 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 


912.G.GPE.7 
10 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 


912.G.GPE.7 
11 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 


912.G.GPE.7 
12 
Geometry 
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 


912.G.GMD.1 
9 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. 


912.G.GMD.1 
10 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. 


912.G.GMD.1 
11 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. 


912.G.GMD.1 
12 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. 


912.G.GMD.2 
9 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. 


912.G.GMD.2 
10 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. 


912.G.GMD.2 
11 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. 


912.G.GMD.2 
12 
Geometry 
Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. 


912.G.GMD.3 
9 
Geometry 
Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 


912.G.GMD.3 
10 
Geometry 
Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 


912.G.GMD.3 
11 
Geometry 
Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 


912.G.GMD.3 
12 
Geometry 
Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 


912.G.GMD.4 
9 
Geometry 
Visualize relationships between twodimensional and threedimensional objects. Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. 


912.G.GMD.4 
10 
Geometry 
Visualize relationships between twodimensional and threedimensional objects. Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. 


912.G.GMD.4 
11 
Geometry 
Visualize relationships between twodimensional and threedimensional objects. Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. 

