Rectangle ABCD is shown below. Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

The following 10 Anchor Papers represent a range of score points and are used in conjunction with the rubrics to assess student responses.

Score for Anchor Paper #1: Rubric Score 1

Annotation: This response demonstrates minimal understanding and analysis of the problem. The student has attempted an inappropriate strategy; three congruent angles will prove similarity - not congruence. No justification for any of the steps is provided.

Score for Anchor Paper #2: Rubric Score 1

Annotation: This response demonstrates minimal understanding and analysis of the problem. The student has an understanding of congruence: "In order for triangle ABD to be congruent to triangle CDB they must have the same angle measurements for each angle and the same length for each side." There is little application of a reasonable strategy. The student states, "angles A and C are 90°," without ever stating that they are congruent or providing justification. The student then states, "the other two angles in that triangle (are) 60° and 30°," without providing support. The student demonstrates some recognition of the need for congruent sides and attempts justification in the statement, "Obviously they have the same length of sides because they wouldn't be able to make a perfect rectangle when put together."

Score for Anchor Paper #3: Rubric Score 1

Annotation: This response demonstrates minimal understanding and analysis of the problem. There is little indication of a reasonable strategy. The diagram shows evidence of congruent parts marked, without statements or justification. The student states, "they both share a common hypotenuse BD," naming a part that could be used in the proof. However, the student has not indicated a strategy to prove the triangles are congruent.

Score for Anchor Paper #4: Rubric Score 2

Annotation: This response demonstrates conceptual understanding and analysis of the problem. The student has an incomplete strategy to prove triangles congruent. Statements and justification for two angles and an indication in the diagram of congruent sides that could be used to prove the triangles congruent are present. However, the student does not state that the triangles are congruent or indicate a congruence theorem.

Score for Anchor Paper #5: Rubric Score 2

Annotation: This response demonstrates a conceptual understanding and analysis of the problem. The student has attempted to prove three corresponding parts congruent in an incomplete application of a reasonable (Angle-Angle-Side) strategy. However, the response has incorrectly cited (Angle-Side-Angle) as its congruence theorem and lacks justification (alternate interior angles) and a step (establishing AD||BC) in order to claim ADB DBC.

Score for Anchor Paper #6: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The student uses an appropriate (Angle-Side-Angle) strategy to prove the triangles congruent. The step establishing AD||BC, in order to claim ADB DBC, is missing. The justification for AB||DC is incorrect.

Score for Anchor Paper #7: Rubric Score 3

Annotation: This response demonstrates a clear understanding and analysis of the problem. The student has attempted an appropriate (Side-Side-Side) strategy to prove the triangles congruent. However, the statement DBDB has the incorrect justification "any segment's parallel to itself," rather than the correct justification of the reflexive property. The justification "def. of rectangle" for the two statements ABDC and ADBC should have more accurately stated that opposite sides of a rectangle are congruent, or cited that this was a property of a rectangle.

Score for Anchor Paper #8: Rubric Score 4

Annotation: This response demonstrates a complete understanding and analysis of the problem. The student has executed a reasonable (Side-Side-Side) strategy for proving congruence. The steps in the proof ("ABDC, because they are opposite sides, ADBC because they too are opposite sides. BDBD, which is true through the Reflexive property of equality.") are clear and logical with all the justification to support the solution.

Score for Anchor Paper #9: Rubric Score 4

Annotation: This response demonstrates complete understanding and analysis of the problem. The student has executed a reasonable (Side-Angle-Side) strategy for proving congruence. The justification, "corresponding sides of rectangle are ," for the two statements ABDC and ADBC should have more accurately stated that opposite sides of a rectangle are congruent. This was not considered to be a significant mathematical error.

Score for Anchor Paper #10: Rubric Score 4

Annotation: This response demonstrates complete understanding and analysis of the problem. The student knows several options to prove congruence: "a triangle must have either 3 sides congruent, 2 angles and a side, angle side angle, or side angle angle." The student clearly and logically executes an appropriate strategy (Angle-Angle-Side), providing justification for each step. The justification, "because they share that side" for "side BD is congruent," could have more accurately cited the reflexive property, but this was not considered to be a significant mathematical error.

Additional Scored Student Responses