Given quadrilateral ABCD with coordinates: A(0, 0), B(r, 0), C(r, m), D(0, m) Which expression proves that ABCD is a rectangle?

The length of each diagonal is √(r² + m²).

The common midpoint of the diagonals is (r/2, m/2).

The slope of AC is m/r and the slope of BD is −m/r.

The length of AB and CD is r, and the length of AD and BC is m.

Geometry · Two- and Three-Dimensional Figures

Virginia SOL G.DF.2

Virginia SOL G.DF.2 is part of the Two- and Three-Dimensional Figures strand in Geometry (Math). Under this Standards of Learning objective, students determine the effect of changing dimensions on three-dimensional figures and describe relationships between original and changed figures. Below is what G.DF.2 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice G.DF.2 for the Virginia SOL test.

Practice G.DF.2 All Geometry standards

What SOL G.DF.2 means

Determine the effect of changing dimensions on three-dimensional figures and describe relationships between original and changed figures.

Practice Geometry SOL questions

Free Geometry questions from official Virginia Department of Education released SOL tests — good practice while you work on G.DF.2 and the rest of the course. Pick an answer to check it instantly, or open “Show answer” to review.

1. A company makes two similar cylindrical containers. The total surface area of the smaller container is 0.81 times that of the larger container. The height of the larger container is 60 centimeters. What is the height of the smaller container?
Show answer
Answer: B — 48.6 cm
2. Given quadrilateral ABCD with coordinates: A(0, 0), B(r, 0), C(r, m), D(0, m) Which expression proves that ABCD is a rectangle?
Show answer
Answer: F — The length of each diagonal is √(r² + m²).
3. A figure is composed of a regular pentagon attached to a rectangle along one side. Angles labeled x are the interior angles of the regular pentagon. What is the measure of each angle labeled x?
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Answer: D — 108°
4. Points Q, R, and S lie on circle P. Angle QPS is a central angle measuring (x + 15)°. The intercepted arc QS measures 40°. What is the value of x?
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Answer: H — 25

→ Take the full free Geometry SOL practice test

Skills you’ll practice for G.DF.2

Describe how changes in one or more dimensions of a figure affect other derived measures (perimeter, area, total surface area, and volume) of the figure.
Describe how changes in surface area and/or volume of a figure affect the measures of one or more dimensions of the figure.
Solve problems, including those in context, involving changing the dimensions or derived measures of a three-dimensional figure.
Compare ratios between side lengths, perimeters, areas, and volumes of similar figures.
Recognize when two- and three-dimensional figures are similar and solve problems, including those in context, involving attributes of similar geometric figures.

Key concepts covered by G.DF.2

dimensional changes
perimeter
area
surface area
volume
surface area changes
volume changes
dimensional measures
derived measures
three-dimensional figures
problem-solving
contextual problems
similar figures
side lengths
perimeters
areas
volumes
ratios
two-dimensional figures

How to study and practice SOL G.DF.2

Start with a quick diagnostic to see whether G.DF.2 is already solid, then work each skill above with guided notes, flashcards, and SOL-style practice questions. For official released items, see our Virginia SOL practice tests guide and how to study for the SOL test.

→ Take the free Geometry SOL practice test

G.DF.1 — Create models and solve problems involving surface area and volume of three-dimensional figures.

Frequently asked questions about SOL G.DF.2

What is Virginia SOL G.DF.2?

SOL G.DF.2 is a Geometry Standard of Learning in the Two- and Three-Dimensional Figures strand. It expects students to determine the effect of changing dimensions on three-dimensional figures and describe relationships between original and changed figures.

What skills does SOL G.DF.2 cover?

SOL G.DF.2 is assessed on 5 skills: describe how changes in one or more dimensions of a figure affect other derived measures (perimeter, area, total surface area, and volume) of the figure; describe how changes in surface area and/or volume of a figure affect the measures of one or more dimensions of the figure; solve problems, including those in context, involving changing the dimensions or derived measures of a three-dimensional figure; compare ratios between side lengths, perimeters, areas, and volumes of similar figures; recognize when two- and three-dimensional figures are similar and solve problems, including those in context, involving attributes of similar geometric figures.

What strand of Geometry is SOL G.DF.2 in?

SOL G.DF.2 belongs to the Two- and Three-Dimensional Figures reporting strand of the Geometry Virginia Standards of Learning.

How do I study and practice for SOL G.DF.2?

Start with a diagnostic to see whether G.DF.2 is already solid, then work the 5 skills above with guided notes, flashcards, and SOL-style practice questions. For official released items, see the Virginia SOL practice tests guide.