Topic outline

  • Chapter 7 - Area

    Standards:

    Given a geometric figure and a rotation, refection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. G-C.5

    Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.1

    Construct and equilateral triangle, a square, and a regular hexagon inscribed in a circle. G-CO.13

    Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. G-GPE.7

    Use geometric shapes, their measures, and their properties to describe objects. G.MG.1

    Derive the formula A = 1/2 ab sine@ for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G-SRT.9

    Use units as a way the understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and origin in graphs and data displays. N-Q.1

    Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events. S-CP.1

     

  • Chapter 8 - Similarity

    Standards:

    Create equations and inequalities in one variable and use them to solve problems. A-CED.1

    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G.GPE.5

    Prove theorems about triangles. G-SRT.4

    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-SRT.5

  • Chapter 9 - Right Triangle Trigonometry

    Standards:

    Prove theorems about triangles. G-SRT.4

    Understand that by similarity, side ratios in right triangles are properties of the angels in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.6

    Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.7

    Use trigonometric shapes, their measures, and their properties to describe objects. G-SRT.8

    Use geometric shapes, their measures, and their properties to describe objects. G-MG.1

    Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes. N-VM.1

    Add and subtract vectors. N-VM.4

    Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. N-VM.4a

     

  • Chapter 10 - Surface Area and Volume

    Standards:

    Give and informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. G-GMD.1

    Give and informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. G-GMD.2

    Use volume formulas for cylinders, pyramids, comes and spheres to solve problems. G-GMD.3

    Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. G-GMD.4

    Use geometry shapes, their measures, and their properties to describe objects. G-MG.1

    Apply concepts of density based on areas and volume in modeling situations. G-MG.2

    Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and origin in graphs and data displays. N-Q.1

  • Chapter 12- Transformations

    Standards:

    Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations the preserve distance and angle to those that do not. G-CO.2

    Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.3

    Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.4

    Given a geometric figure and a rotation, reflection, or translations, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G-CO.5

    Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; give two figures, use the definition of congruence in terms of rigid motions to decide if the are congruent. G-CO.6

  • Chapter 11- Circles

    Standards: 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. G-C.2

    Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G-C.3

    Construct a tangent line from a point outside a given circle to the circle. G-C.4(+)

    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. G-GPE.1

    Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. G-GMD.4