BPS District Mathematics Standards Book
Math Learning Progressions
[G] Geometry
Math Learning Progressions HS Math Concepts
[G] Geometry
Studentsâ€™ 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 realworld 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 reallife 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 twodimensional and threedimensional objects.
Modeling with Geometry
 Apply geometric concepts in modeling situations
MATHS.G [G] Overview: Geometry
MATHS.GCO Domain: [GCO] Congruence

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

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

 MATHS.GC.01 Prove all circles are similar
 MATHS.GC.02 Identify and describe relationships among inscribed angles, radii, and chords
 MATHS.GC.03 Construct the inscribed and circumscribed circles of a triangle
 MATHS.GC.04 Construct a tangent line from a point outside a given circle to the circle
 MATHS.GC.05 Show the length of the arc intercepted by an angle proportional to the radius
MATHS.GGPE Domain: [GGPE] Expressing Geometric Properties with Equations

 MATHS.GGPE.01 Use Pythagorean Theorem to derive the equation of a circle
 MATHS.GGPE.02 Derive the equation of a parabola given a focus and directrix
 MATHS.GGPE.03 Derive the equations of ellipses and hyperbolas given foci, using the fact
 MATHS.GGPE.04 Use coordinates to prove simple geometric theorems algebraically
 MATHS.GGPE.05 Prove the slope criteria for parallel and perpendicular lines
 MATHS.GGPE.06 Find the point on a line between two points that partitions it in a given ratio
 MATHS.GGPE.07 Use coordinates to compute perimeter of polygons, area of triangles/rectangles
MATHS.GGMD Domain: [GGMD] Geometric Measurement and Dimension

 MATHS.GGMD.01 Support formulas for circumference/area(circle) & volume(cylinder/pyramid/cone)
 MATHS.GGMD.02 Give an informal argument using Cavalieri's principle for the formulas for
 MATHS.GGMD.03 Use volume formulas for cylinders, pyramids, cones, and spheres
 MATHS.GGMD.04 Identify the shapes of 2D crosssections of 3D objects
MATHS.GMG Domain: [GMG] Modeling with Geometry

 MATHS.GMG.01 Use geometric shapes, measures, and properties to describe objects
 MATHS.GMG.02 Apply concepts of density based on area and volume in modeling situations
 MATHS.GMG.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 twodimensional and threedimensional objects.
Modeling with Geometry
 Apply geometric concepts in modeling situations