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MAFS.912.G-CO.3.9

Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Prove geometric theorems. (Geometry - Major 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: DDHT , EE item(s)

  • Assessment Limits :
    Items may assess relationships between vertical angles, special angles
    formed by parallel lines and transversals, angle bisectors, congruent
    supplements, congruent complements, and a perpendicular bisector
    of a line segment.

    Items may have multiple sets of lines and angles.

    Items may include narrative proofs, flow-chart proofs, two-column
    proofs, or informal proofs.

    In items that require the student to justify, the student should not be
    required to recall from memory the formal name of a theorem.

  • Calculator :

    Neutral

  • Clarification :
    Students will prove theorems about lines.

    Students will prove theorems about angles.

    Students will use theorems about lines to solve problems.

    Students will use theorems about angles to solve problems.

  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context. 
  • Response Attributes :
    Items may require the student to give statements and/or
    justifications to complete formal and informal proofs.

    Items may require the student to justify a conclusion from a
    construction.



     

SAMPLE TEST ITEMS (2)

  • Test Item #: Sample Item 1
  • Question:

    In the figure, begin mathsize 12px style stack A B with left right arrow on top space parallel to space stack C D with left right arrow on top space a n d space stack B C with left right arrow on top space parallel to space stack A E with left right arrow on top end style. Let begin mathsize 12px style angle A B D end style measure (3x+4)º, begin mathsize 12px style angle B C D end style measure(6x-8)º, and begin mathsize 12px style angle E D F end style measure (7x-20)º.

    Click on the blank to enter the degree measure that completes the equation shown.

     

  • Difficulty: N/A
  • Type: EE: Equation Editor