BPS District Mathematics Standards

Math Learning Progressions

[G] Geometry

Students’ prior knowledge includes:

  • Students understand congruence and similarity using physical models, transparencies, or geometry software (grade 8)
  • Students understand and apply the Pythagorean Theorem (grade 8)
  • Student solve real-world and mathematical problems involving volume of cylinders, cones and spheres (grade 8)
  • Students draw, construct and describe geometrical figures and describe the relationships between them (grade 7)
  • Students solve real-life and mathematical problems involving angle measures, area, surface area, and volume (grade 7)
Congruence
  • Experiment with transformations in the plane.
  • Understand congruence in terms of rigid motions.
  • Prove and apply geometric theorems.
  • Make geometric constructions.
Similarity, Right Triangles, and Trigonometry
  • Understand similarity.
  • Prove theorems involving similarity.
  • Define trigonometric ratios and solve problems involving right triangles.
  • Apply trigonometry to general triangles.
Circles
  • Understand and apply theorems involving circles.
  • Find arc lengths and areas of sectors of circles.
Expressing Geometric Properties with Equations
  • Understand and use conic sections.
  • Use coordinates to verify simple geometric theorems algebraically
Geometric Measurement and Dimension
  • Explain surface area and volume formulas and use them to solve problems.
  • Visualize relationships between two-dimensional and three-dimensional objects.
Modeling with Geometry
  • Apply geometric concepts in modeling situations

MAT-HS.G [G] Overview: Geometry

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

 

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.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

Congruence

  • Experiment with transformations in the plane.
  • Understand congruence in terms of rigid motions.
  • Prove and apply geometric theorems.
  • Make geometric constructions

Similarity, Right Triangles, and Trigonometry

  • Understand similarity.
  • Prove theorems involving similarity.
  • Define trigonometric ratios and solve problems involving right triangles.
  • Apply trigonometry to general triangles.

Circles

  • Understand and apply theorems involving circles.
  • Find arc lengths and areas of sectors of circles.

Expressing Geometric Properties with Equations

  • Understand and use conic sections.
  • Use coordinates to verify simple geometric theorems algebraically.

Geometric Measurement and Dimension

  • Explain surface area and volume formulas and use them to solve problems.
  • Visualize relationships between two-dimensional and three-dimensional objects.

Modeling with Geometry

  • Apply geometric concepts in modeling situations