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MAFS.912.G-C.1.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Circles
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Understand and apply theorems about circles. (Geometry - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

TEST ITEM SPECIFICATIONS

  • Item Type(s): This benchmark may be assessed using: GRID item(s)

  • Assessment Limits :
    Items may include problems that use the incenter and circumcenter
    of a triangle. 
  • Calculator :

    Neutral

  • Clarification :
    Students will construct a circle inscribed inside a triangle.

    Students will construct a circle circumscribed about a triangle.

    Students will solve problems using the properties of inscribed and
    circumscribed circles of a triangle.

    Students will use or justify properties of angles of a quadrilateral that
    is inscribed in a circle.

  • Stimulus Attributes :
    Item may be set in real-world or mathematical context.
  • Response Attributes :
    Items may require the student to use or choose the correct unit of
    measure.

    Items may require the student to provide steps for a construction.

    Items may require the student to give statements and/or
    justifications to complete formal and informal proofs.

SAMPLE TEST ITEMS (1)

  • Test Item #: Sample Item 1
  • Question:

    Trapezoid ABCD is inscribed in circle O. Diagonals begin mathsize 12px style stack B D with bar on top space a n d space stack A C with bar on top end style meet at point E and begin mathsize 12px style stack A D with bar on top end style is parallel to begin mathsize 12px style stack B C with bar on top end style, as shown.

    Select the angles and value that make a true statement about trapezoid ABCD.

  • Difficulty: N/A
  • Type: GRID: Graphic Response Item Display