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View all PreK-12 NYS Learning Standards in a dropdown list format.
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  • Standard Area - TECH: Learning Standards for Technology
    (see MST standards under Previous Standard Versions)
        • Introduction - MST3.G.Introduction: Integrated Geometry

          In implementing the Geometry process and content performance indicators, it is expected that students will identify and justify geometric relationships, formally and informally. For example, students will begin with a definition of a figure and from that definition, students will be expected to develop a list of conjectured properties of the figure and to justify each conjecture informally or with formal proof. Students will also be expected to list the assumptions that are needed in order to justify each conjectured property and present their findings in an organized manner.

          The intent of both process and content performance indicators is to provide a variety of ways for students to acquire and demonstrate mathematical reasoning ability when solving problems. The variety of approaches to verification and proof is what gives curriculum developers and teachers the flexibility to adapt strategies to address these performance indicators in a manner that meets the diverse needs of out students. Local curriculum and local/state assessments must support and allow students to use any mathematically correct method when solving a problem.

          Throughout this document the performance indicators use the words investigate, explore, discover, conjecture, reasoning, argument, justify, explain, proof, and apply. Each of these terms is an important component in developing a student's mathematical reasoning ability. It is therefore important that a clear and common definition of these terms be understood. The order of these terms reflects different stages of the reasoning process.

          Investigate/Explore - Students will be given situations in which they will be asked to look for patterns or relationships between elements within the setting.

          Discover - Students will make note of possible relationships of perpendicularity, parallelism, congruence, and/or similarity after investigation/exploration.

          Conjecture - Students will make an overall statement, thought to be true, about the new discovery.

          Reasoning - Students will engage in a process that leads to knowing something to be true or false.

          Argument - Students will communicate, in verbal or written form, the reasoning process that leads to a conclusion. A valid argument is the end result of the conjecture/reasoning process.

          Justify/Explain - Students will provide an argument for a mathematical conjecture. It may be an intuitive argument or a set of examples that support the conjecture. the argument may include, but is not limited to, a written paragraph, measurement using appropriate tools, the use of dynamic software, or a written proof.

          Proof - Students will present a valid argument, expressed in written form, justified by axioms, definitions, and theorem using properties of perpendicularity, parallelism, congr

          • Assessments
          • Performance Indicator - MST3.G.G.24:
            Students determine the negation of a statement and establish its truth value.
            Assessments
          • Performance Indicator - MST3.G.G.25:
            Students know and apply the conditions under which a compound statement (conjunction, disjunction, conditional, biconditional) is true.
            Assessments
          • Performance Indicator - MST3.G.G.26:
            Identify and write the inverse, converse, and contrapositive of a given conditional statement and note the logical equivalences.
            Assessments
          • Performance Indicator - MST3.G.G.27:
            Students write a proof arguing from a given hypothesis to a given conclusion.
            Educational Resources Assessments
          • Performance Indicator - MST3.G.G.28:
            Students determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.29:
            Students identify corresponding parts of congruent triangles.
            Educational Resources Assessments
          • Performance Indicator - MST3.G.G.30:
            Students investigate, justify, and apply theorems about the sum of the measures of the angles of a triangle.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.31:
            Students investigate, justify, and apply the isosceles triangle theorem and its converse.
            Assessments Common Core
          • Performance Indicator - MST3.G.G.32:
            Students investigate, justify, and apply theorems about geometric inequalities, using the exterior angle theorem.
            Assessments
          • Performance Indicator - MST3.G.G.33:
            Students investigate, justify, and apply the triangle inequality theorem.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.34:
            Students determine either the longest side of a triangle given the three angle measures or the largest angle given the lengths of three sides of a triangle.
            Assessments
          • Performance Indicator - MST3.G.G.35:
            Students determine if two lines cut by a transversal are parallel, based on the measure of given pairs of angles formed by the transversal and the lines.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.36:
            Students investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons.
            Assessments
          • Performance Indicator - MST3.G.G.37:
            Students investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons.
            Educational Resources Assessments
          • Performance Indicator - MST3.G.G.38:
            Students investigate, justify, and apply theorems about parallelograms involving their angles, sides, and diagonals.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.39:
            Students investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses, squares) involving their angles, sides, and diagonals.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.40:
            Students investigate, justify, and apply theorems about trapezoids (including isosceles trapezoids) involving their angles, sides, medians, and diagonals.
            Educational Resources Assessments
          • Performance Indicator - MST3.G.G.41:
            Students justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or trapezoids.
            Educational Resources Assessments
          • Performance Indicator - MST3.G.G.42:
            Students investigate, justify, and apply theorems about geometric relationships, based on the properties of the line segment joining the midpoints of two sides of the triangle.
            Assessments Common Core
          • Performance Indicator - MST3.G.G.43:
            Students investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1.
            Assessments Common Core
          • Performance Indicator - MST3.G.G.44:
            Students establish similarity of triangles, using the following theorems: AA, SAS, and SSS.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.45:
            Students investigate, justify, and apply theorems about similar triangles.
            Educational Resources Assessments Common Core
          • Performance Indicator - MST3.G.G.46:
            Students investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle.
            Assessments Common Core
          • Performance Indicator - MST3.G.G.47:

            Students investigate, justify, and apply theorems about mean proportionality:

          • the altitude to the hypotenuse of a right triangle is the mean proportional between the two segments along the hypotenuse
          • the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either leg of the right triangle is the mean proportional between the hypotenuse and segment of the hypotenuse adjacent to that leg
        Assessments Common Core
    • Performance Indicator - MST3.G.G.48:
      Students investigate, justify, and apply the Pythagorean theorem and its converse.
      Educational Resources Assessments Common Core
    • Performance Indicator - MST3.G.G.49:

      Students investigate, justify, and apply theorems regarding chords of a circle::

    • perpendicular bisectors of chords
    • the relative lengths of chords as compared to their distance from the center of the circle
Educational Resources Assessments Common Core
  • Performance Indicator - MST3.G.G.50:

    Students investigate, justify, and apply theorems about tangent lines to a circle:

  • a perpendicular to the tangent at the point of tangency
  • two tangents to a circle from the same external point
  • common tangents of two non-intersecting or tangent circles
    • Assessments Common Core
  • Performance Indicator - MST3.G.G.51:

    Students investigate, justify, and apply theorems about the arcs determined by the rays of angles formed by two lines intersecting a circle when the vertex is:

  • inside the circle (two chords)
  • on the circle (tangent and chord)
  • outside the circle (two tangents, two secants, or tangent and secant)
    • Assessments Common Core
  • Performance Indicator - MST3.G.G.52:
    Students investigate, justify, and apply theorems about arcs of a circle cut by two parallel lines.
    Assessments Common Core
  • Performance Indicator - MST3.G.G.53:

    Students investigate, justify, and apply theorems regarding segments intersected by a circle:

  • along two tangents from the same external point
  • along two secants from the same external point
  • along a tangent and a secant from the same external point
  • along two intersecting chords of a given circle
    • Educational Resources Assessments
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