MAT-HS.G [G] Overview: Geometry

MAT-HS.G-CO Domain: [G-CO] Congruence

• • MAT-HS.G-CO.01 Know definitions of angle/circle/perpendicular line/parallel line/line segment
  • MAT-HS.G-CO.02 Represent, describe, compare transformations in the plane
  • MAT-HS.G-CO.03 Describe the rotations and reflections that carry a polygon onto itself
  • MAT-HS.G-CO.04 Develop definitions of rotations, reflections, and translations
  • MAT-HS.G-CO.05 Given a figure and rotation/reflection/translation, draw the transformed figure
  • MAT-HS.G-CO.06 Use descriptions of rigid motions and congruence to transform figures
  • MAT-HS.G-CO.07 Use the definition of congruence to show that two triangles are congruent
  • MAT-HS.G-CO.08 Explain the definition of triangle congruence in terms of rigid motions
  • MAT-HS.G-CO.09 Prove theorems about lines and angles
    • MAT-HS.G-CO.09.a Prove theorems about lines and angles
    • MAT-HS.G-CO.09.b Apply theorems about lines and angles
  • MAT-HS.G-CO.10 Prove theorems about triangles
    • MAT-HS.G-CO.10.a Prove theorems about triangles
    • MAT-HS.G-CO.10.b Apply theorems about triangles
  • MAT-HS.G-CO.11 Prove theorems about parallelograms
    • MAT-HS.G-CO.11.a Prove theorems about parallelograms
    • MAT-HS.G-CO.11.b Apply theorems about parallelograms
  • MAT-HS.G-CO.12 Make formal geometric constructions with a variety of tools and methods
  • MAT-HS.G-CO.13 Construct an equilateral triangle/square/regular hexagon inscribed in a circle

MAT-HS.G-SRT Domain: [G-SRT] Similarity, Right Triangles, and Trigonometry

• • MAT-HS.G-SRT.01 Verify experimentally the properties of dilations
    • G-SRT.01.a A line not passing through the center to a parallel line, center line unchanged
    • G-SRT.01.b A line segment is longer or shorter in the ratio given by the scale factor
  • MAT-HS.G-SRT.02 Use definition of similarity/transformations to see if 2 figures are similar
  • MAT-HS.G-SRT.03 Use similarity transformations to establish the AA criterion for two triangles
  • MAT-HS.G-SRT.04 Prove theorems about triangles
  • MAT-HS.G-SRT.05 Use congruence/similarity criteria to solve problems and to prove relationships
    • MAT-HS.G-SRT.05.a Use congruence to solve problems in geometric figures
    • MAT-HS.G-SRT.05.b Use similarity criteria to solve problems in geometric figures
    • MAT-HS.G-SRT.05.c Use similarity criteria to prove relationships in geometric figures
  • MAT-HS.G-SRT.06 Understand that side ratios in right triangles are properties of the angles
  • MAT-HS.G-SRT.07 Explain the relationship between the sine and cosine of complementary angles
  • MAT-HS.G-SRT.08 Apply trigonometric ratios and the Pythagorean Theorem to solve right triangles
    • MAT-HS.G-SRT.08.a Apply trigonometric ratios and the Pythagorean Theorem to solve right triangles
    • MAT-HS.G-SRT.08.b Apply trigonometric ratios and the Pythagorean Theorem to solve special triangles
  • MAT-HS.G-SRT.09 Derive the formula A = 1/2 ab sin( C ) for the area of a triangle
  • MAT-HS.G-SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems
  • MAT-HS.G-SRT.11 Apply the Law of Sines and the Law of Cosines to find unknown measurements

MAT-HS.G-C Domain: [G-C] Circles

• • MAT-HS.G-C.01 Prove all circles are similar
  • MAT-HS.G-C.02 Identify and describe relationships among inscribed angles, radii, and chords
  • MAT-HS.G-C.03 Construct the inscribed and circumscribed circles of a triangle
  • MAT-HS.G-C.04 Construct a tangent line from a point outside a given circle to the circle
  • MAT-HS.G-C.05 Show the length of the arc intercepted by an angle proportional to the radius

MAT-HS.G-GPE Domain: [G-GPE] Expressing Geometric Properties with Equations

• • MAT-HS.G-GPE.01 Use Pythagorean Theorem to derive the equation of a circle
  • MAT-HS.G-GPE.02 Derive the equation of a parabola given a focus and directrix
  • MAT-HS.G-GPE.03 Derive the equations of ellipses and hyperbolas given foci, using the fact
  • MAT-HS.G-GPE.04 Use coordinates to prove simple geometric theorems algebraically
  • MAT-HS.G-GPE.05 Prove the slope criteria for parallel and perpendicular lines
  • MAT-HS.G-GPE.06 Find the point on a line between two points that partitions it in a given ratio
  • MAT-HS.G-GPE.07 Use coordinates to compute perimeter of polygons, area of triangles/rectangles

MAT-HS.G-GMD Domain: [G-GMD] Geometric Measurement and Dimension

• • MAT-HS.G-GMD.01 Support formulas for circumference/area(circle) & volume(cylinder/pyramid/cone)
  • MAT-HS.G-GMD.02 Give an informal argument using Cavalieri's principle for the formulas for
  • MAT-HS.G-GMD.03 Use volume formulas for cylinders, pyramids, cones, and spheres
  • MAT-HS.G-GMD.04 Identify the shapes of 2D cross-sections of 3D objects

MAT-HS.G-MG Domain: [G-MG] Modeling with Geometry

• • MAT-HS.G-MG.01 Use geometric shapes, measures, and properties to describe objects
  • MAT-HS.G-MG.02 Apply concepts of density based on area and volume in modeling situations
  • MAT-HS.G-MG.03 Apply geometric methods to solve design problems

A Sample of HS Math Concept Geometry to Become Ready for College and Career