




Massachusetts Comprehensive Assessment System
2016, Grade 10 Mathematics
Question 20: OpenResponse 

Reporting Category: Geometry Standard: 10.G.6  Use the properties of special triangles (e.g., isosceles, equilateral, 30°60°90°, 45°45°90°) to solve problems. Standard: Mathematics.G.SRT.3.06  Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 
The diagram below shows rhombus ABCD with a side length of 8 centimeters.  What is the perimeter, in centimeters, of rhombus ABCD? Show or explain how you got your answer.
The measure of is 60°.  What is the length, in centimeters, of diagonal ? Show or explain how you got your answer.
 What is the length, in centimeters, of diagonal ? Show or explain how you got your answer.
 What is the area, in square centimeters, of rhombus ABCD? Show or explain how you got your answer.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Geometry concepts involved in understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle. The student determines the lengths of the diagonals of a rhombus and uses them to determine its area. 
4 
3 
The student response demonstrates a good understanding of the Geometry concepts involved in understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points. 
2 
The student response demonstrates a fair understanding of the Geometry concepts involved in understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates a minimal understanding of the Geometry concepts involved in understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle. 
0 
The student response contains insufficient evidence of an understanding of the Geometry concepts involved in understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Algebra and Functions
 Question 20: Geometry
 Question 21: Number and Quantity
 Question 36: Algebra and Functions
 Question 41: Statistics and Probability
 Question 42: Geometry
Return to the MCAS 2016 Student Work Directory
Last Updated: August 15, 2018


