Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
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 assess theorems and their converses for interior triangle
    sum, base angles of isosceles triangles, mid-segment of a triangle,
    concurrency of medians, concurrency of angle bisectors, concurrency
    of perpendicular bisectors, triangle inequality, and the Hinge

    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 triangles.

    Students will use theorems about triangles 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


  • Test Item #: Sample Item 1
  • Question:

    Drag statements from the statements column and reasons from the reasons column to their correct location to complete the proof.

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