Standards Map

Mathematics > Grade 8 > Geometry
Accessibility Mode: Note: You are viewing this information in accessibility mode. To view the map, enlarge your window or use a larger device.

Mathematics | Grade : 8

Domain - Geometry

Cluster - Understand and apply the Pythagorean Theorem.

[8.G.B.8] - Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Resources:


  • Pythagorean Theorem
    For any right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse.

Predecessor Standards:

  • 6.G.A.3
    Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Successor Standards:

  • GEO.G-GPE.A.1
    Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
  • GEO.G-GPE.A.2
    Derive the equation of a parabola given a focus and directrix.
  • GEO.G-GPE.B.4
    Use coordinates to prove simple geometric theorems algebraically, including the distance formula and its relationship to the Pythagorean Theorem. 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).
  • GEO.G-GPE.B.7
    Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula).*
  • MI.G-GPE.B.7
    Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula).*
  • MII.G-GPE.A.1
    Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
  • MII.G-GPE.A.2
    Derive the equation of a parabola given a focus and directrix.
  • MII.G-GPE.B.4
    Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. 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).
  • PC.G-GPE.A.3
    (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
  • PC.G-GPE.A.3.a
    (+) Use equations and graphs of conic sections to model real-world problems.*
  • AQR.G-GPE.A.3
    (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
  • AQR.G-GPE.A.3.a
    (+) Use equations and graphs of conic sections to model real-world problems.*

Same Level Standards:

  • 8.G.B.7
    Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.