Prove theorems about parallelograms; use theorems about parallelograms to solve problems. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
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


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

  • Assessment Limits :
    Items may require the student to be familiar with similarities and
    differences between types of parallelograms (e.g., squares and

    Items may require the student to identify a specific parallelogram.

    Items may assess theorems and their converses for opposite sides of
    a parallelogram, opposite angles of a parallelogram, diagonals of a
    parallelogram, and consecutive angles of a parallelogram.

    Items may assess theorems and their converses for rectangles and

    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 :


  • Clarification :
    Students will prove theorems about parallelograms.

    Students will use properties of parallelograms to solve problems.

  • Stimulus Attributes :
    Items may be set in real-world or mathematical context.
  • Response Attributes :
    Items may require the student to classify a quadrilateral as a
    parallelogram based on given properties or measures.

    Items may require the student to prove that a quadrilateral is a


  • Test Item #: Sample Item 1
  • Question:

    Drag the correct statement from the statements column and the correct reasons from the reasons column to the table to complete line 3 of the proof.

  • Difficulty: N/A
  • Type: DDHT: Drag-and-Drop Hot Text