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