MA.912.G.3.4Archived Standard

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Prove theorems involving quadrilaterals.

Remarks

Example: Prove that the diagonals of a rectangle are congruent.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Idea: Level 3: Strategic Thinking & Complex Reasoning
Standard: Quadrilaterals - Classify and understand relationships among quadrilaterals (rectangle, parallelogram, kite, etc.). Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas, and prove theorems involving quadrilaterals.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , FR item(s)
    • Also Assesses:

    MA.912.D.6.4 Use methods of direct and indirect proof and determine whether a short proof is logically valid.

    MA.912.G.3.1 Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite.

    MA.912.G.3.2 Compare and contrast special quadrilaterals on the basis of their properties.

    MA.912.G.8.5 Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.
  • Clarification :
    Students will use geometric properties to justify measures and characteristics of quadrilaterals.
  • Content Limits :
    Items may require statements and/or justifications to complete formal and informal proofs.
  • Stimulus Attributes :

    Items may be set in either mathematical or real-world contexts.

    Graphics should be used in these items, as appropriate.

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question:

     

    Which statement best explains why the equation x + 5 = 2x  3 can be used to solve for x?

  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question:

    Four students are choreographing their dance routine for the high school talent show. The stage is rectangular and measures 15 yards by 10 yards. The stage is represented by the coordinate grid below. Three of the students—Riley (R), Krista (K), and Julian (J)—graphed their starting positions, as shown below. Let H represent Hannah’s starting position on the stage.

     

    What should be the x-coordinate of point H so that RKJH is a parallelogram?

  • Difficulty: N/A
  • Type: FR: Fill-in Response

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