### Descriptive Statements:

- Analyze the use of various units and unit conversions within the customary and metric systems.
- Apply the concepts of similarity, scale factors, and proportional reasoning to solve measurement problems.
- Analyze precision, error, and rounding in measurements and computed quantities.
- Apply the concepts of perimeter, circumference, area, surface area, and volume to solve real-world problems.

### Sample Item:

### Descriptive Statements:

- Demonstrate knowledge of axiomatic systems and of the axioms of non-Euclidean geometries.
- Use the properties of polygons and circles to solve problems.
- Apply the Pythagorean theorem and its converse.
- Analyze formal and informal geometric proofs, including the use of similarity and congruence.
- Use nets and cross sections to analyze three-dimensional figures.

### Sample Item:

In the proof above, steps 2 and 4 are missing. Which of the following reasons justifies step 5?

- AAS
- ASA
- SAS
- SSS

Correct Response and Explanation (ShowHide)

**C. ** This question requires the examinee to analyze formal and informal geometric proofs, including the use of similarity and congruence. The side-angle-side (SAS) theorem can be used to show that Δ*ABC* and Δ*CDA* are congruent if each has two sides and an included angle that are congruent with two sides and an included angle of the other. In the diagram *AB* and *DC* are given as congruent, and the missing statement 2 is that *AC* is congruent to itself by the reflexive property of equality. The included angles ∠*BAC* and ∠*DCA* are congruent because they are alternate interior angles constructed by the transversal *AC* that crosses the parallel line segments *AB* and *DC*. Thus Δ*ABC* and Δ*CDA* meet the requirements for using SAS to prove congruence.

### Descriptive Statements:

- Analyze two- and three-dimensional figures using coordinate systems.
- Apply concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane.
- Analyze conic sections.
- Determine the effects of geometric transformations on the graph of a function or relation.
- Analyze transformations and symmetries of figures in the coordinate plane.

### Sample Item:

The vertices of triangle *ABC* are *A*(–5, 3), *B*(2, 2), and *C*(–1, –5). Which of the following is the length of the median from vertex *B* to side *AC?*

- 4

Correct Response and Explanation (ShowHide)

**C. ** This question requires the examinee to apply concepts of distance, midpoint,
and slope to classify figures and solve problems in the coordinate plane. The midpoint of side *AC* where its median intersects is computed as = (–3, –1). The distance from *B*(2, 2) to (–3, –1) is computed as *d* = .