Math Common Core - Alignment with Math Open Reference

The Common Core State Standards Initiative is an education initiative in the United States that details what K-12 students should know in English and Math at the end of each grade year, and seeks to establish conformity in education standards across the US.

The document below is a reproduction of the relevant parts of the common core geometry standards. Wherever there are relevant pages in Math Open Reference, the appropriate text is a link to those pages. It is designed to make it easy for teachers and parents to find useful resources to help teach and coach students.

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Congruence G CO
Experiment with transformations in the plane.
Understand congruence in terms of rigid motions.
Prove geometric theorems.
Make geometric constructions.
  2. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Similarity, Right Triangles, and Trigonometry G SRT
Understand similarity in terms of similarity transformations.
  1. Verify experimentally the properties of dilations given by a center and a scale factor:
    1. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
  3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarity.
  2. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles.
  2. Explain and use the relationship between the sine and cosine of complementary angles.
  3. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
8.1 Derive and use the trigonometric ratios for special right triangles ( 30°- 60°- 90° and 45°- 45°- 90°) CA
Apply trigonometry to general triangles.
  1. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  2. (+) Prove the Law of Sines and Law of Cosines and use them to solve problems.
CirclesG C
Understand and apply theorems about circles.
  1. Prove that all circles are similar.
  3. Construct the inscribed circle and circumscribed circle of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Find arc lengths and areas of sectors of circles.
  1. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [Convert between degrees and radians. CA]
Expressing Geometric Properties with EquationsG GPE
3.1 Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola and graph the equation. CA
Use coordinates to prove simple geometric theorems algebraically.
  1. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2).
Geometric Measurement and DimensionG GMD
Explain volume formulas and use them to solve problems.
  3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Visualize relationships between two-dimensional and three-dimensional objects.
  2. Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k2 , and k3 ,respectively; determine length, area and volume measures using scale factors. CA
  3. Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems. CA
Modeling with GeometryG MG
Apply geometric concepts in modeling situations.


This Common Core alignment document was created by Patrick Beal, an educational consultant from southern California. He can be contacted at