Prove that all circles are similar using similarity
Prove that all circles are similar using similarity transformations.
G.C.A.2
Identify and describe relationships among inscribed angles, radii
Identify and describe relationships among inscribed angles, radii and chords of circles.
G.C.A.3
Construct the inscribed and circumscribed circles of a
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
G.C.B.4
Derive the formula for the length of an
Derive the formula for the length of an arc of a circle.
G.C.B.5
Derive the formula for the area of a
Derive the formula for the area of a sector of a circle.
📌Conditional Probability and Rules of Probability (G.CP)8 standards
G.CP.A.1
Describe events as subsets of a sample space
Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections or complements of other events.
G.CP.A.2
Understand the definition of independent events and use
Understand the definition of independent events and use it to solve problems.
G.CP.A.3
Calculate conditional probabilities of events
Calculate conditional probabilities of events.
G.CP.A.4
Construct and interpret two-way frequency tables of data
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
G.CP.A.5
Recognize and explain the concepts of conditional probability
Recognize and explain the concepts of conditional probability and independence in a context.
G.CP.A.6
Apply and interpret the Addition Rule for calculating
Apply and interpret the Addition Rule for calculating probabilities.
G.CP.A.7
Apply and Interpret the general Multiplication Rule in
Apply and Interpret the general Multiplication Rule in a uniform probability model.
G.CP.A.8
Use permutations and combinations to solve problems
Use permutations and combinations to solve problems.
📌Congruence (G.CO)11 standards
G.CO.A.1
Define angle, circle, perpendicular line, parallel line, line
Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.
G.CO.A.2
Represent transformations in the plane, and describe them
Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs.
G.CO.A.3
Describe the rotational symmetry and lines of symmetry
Describe the rotational symmetry and lines of symmetry of two-dimensional figures.
G.CO.A.4
Develop definitions of rotations, reflections and translations in
Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
G.CO.A.5
Demonstrate the ability to rotate, reflect or translate
Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.
G.CO.B.6
Develop the definition of congruence in terms of
Develop the definition of congruence in terms of rigid motions.
G.CO.B.7
Develop the criteria for triangle congruence from the
Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.
G.CO.C.8
Prove theorems about lines and angles
Prove theorems about lines and angles.
G.CO.C.9
Prove theorems about triangles
Prove theorems about triangles.
G.CO.C.10
Prove theorems about polygons
Prove theorems about polygons.
G.CO.D.11
Construct geometric figures using various tools and methods
Construct geometric figures using various tools and methods.
📌Exploring Geometric Properties with Equations (G.GPE)6 standards
G.GPE.A.1
Derive the equation of a circle
Derive the equation of a circle.
G.GPE.A.2
Derive the equation of a parabola given a
Derive the equation of a parabola given a focus and directory.
G.GPE.B.3
Use coordinates to prove geometric theorems algebraically
Use coordinates to prove geometric theorems algebraically.
G.GPE.B.4
Prove the slope criteria for parallel and perpendicular
Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.
G.GPE.B.5
Find the point on a directed line segment
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.GPE.B.6
Use coordinates to compute perimeters of polygons and
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
📌Geometric Measurement and Dimension. (G.GMD)4 standards
G.GMD.A.1
Give an informal argument for the formulas for
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone.
G.GMD.A.2
Use volume formulas for cylinders, pyramids, cones, spheres
Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.
G.GMD.B.3
Identify the shapes of two-dimensional cross-sections of three-dimensional
Identify the shapes of two-dimensional cross-sections of three-dimensional objects.
G.GMD.B.4
Identify three-dimensional objects generated by transformations of two-dimensional
Identify three-dimensional objects generated by transformations of two-dimensional objects.
📌Modeling with Geometry (G.MG)3 standards
G.MG.A.1
Use geometric shapes, their measures and their properties
Use geometric shapes, their measures and their properties to describe objects.
G.MG.A.2
Apply concepts of density based on area and
Apply concepts of density based on area and volume in modeling situations.
G.MG.A.3
Apply geometric methods to solve design mathematical modeling
Apply geometric methods to solve design mathematical modeling problems.
📌Similarity, Right Triangles, and Trigonometry (G.SRT)8 standards
G.SRT.A.1
Construct and analyze scale changes of geometric figures
Construct and analyze scale changes of geometric figures.
G.SRT.A.2
Use the definition of similarity to decide if
Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.
G.SRT.A.3
Use the properties of similarity transformations to establish
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.B.4
Use congruence and similarity criteria for triangles to
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G.SRT.C.5
Understand that side ratios in right triangles define
Understand that side ratios in right triangles define the trigonometric ratios for acute angles.
G.SRT.C.6
Explain and use the relationship between the sine
Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.C.7
Use trigonometric ratios and the Pythagorean Theorem to
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.
G.SRT.C.8
Derive the formula A = 1/2 ab sin
Derive the formula A = 1/2 ab sin(C) for the area of a triangle.