Geometry · Polygons and Circles
Virginia SOL G.PC.3
Virginia SOL G.PC.3 is part of the Polygons and Circles strand in Geometry (Math). Under this Standards of Learning objective, students solve problems involving properties of circles. Below is what G.PC.3 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice G.PC.3 for the Virginia SOL test.
What SOL G.PC.3 means
Solve problems involving properties of circles.
Practice Geometry SOL questions
Free Geometry questions from official Virginia Department of Education released SOL tests — good practice while you work on G.PC.3 and the rest of the course. Pick an answer to check it instantly, or open “Show answer” to review.
1. Which value for x is a counterexample to the following statement? For all positive values of x, x² > x.
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Answer: B — −0.1
2. The following information describes a Venn diagram showing lunch selections made by athletes. • A total of 310 athletes selected a sandwich. • A total of 125 athletes selected both a sandwich and a salad. • A total of 180 athletes selected both a sandwich and a soup. • The total number of athletes who selected a sandwich includes those who may also have selected salad, soup, or both. How many athletes selected a sandwich, a soup, and a salad?
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Answer: H — 65
3. The following information represents a Venn diagram of triangles. • One circle represents Acute Triangles. • One circle represents Isosceles Triangles. • The two circles overlap. Which statement is valid?
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Answer: D — Some triangles are both acute and isosceles.
4. Lines j and k are cut by transversals m and n. Three angles are formed with the following measures: • One angle measures (x + y)°. • A corresponding angle on the same transversal measures (x + 30)°. • Another angle formed by the second transversal measures (3x − y − 60)°. Which relationship is sufficient to prove that j ∥ k?
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Answer: C — y = x − 30
Skills you’ll practice for G.PC.3
- Determine the proportional relationship between the arc length or area of a sector and other parts of a circle.
- Solve for arc measures and angles in a circle formed by central angles.
- Solve for arc measures and angles in a circle involving inscribed angles.
- Calculate the length of an arc of a circle.
- Calculate the area of a sector of a circle.
- Apply arc length or sector area to solve for an unknown measurement of the circle, including the radius, diameter, arc measure, central angle, arc length, or sector area.
Key concepts covered by G.PC.3
- arc length
- sector area
- circle proportions
- central angles
- arc measures
- circle angles
- inscribed angles
- circle
- unknown measurements
How to study and practice SOL G.PC.3
Start with a quick diagnostic to see whether G.PC.3 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.
Related Geometry standards in Polygons and Circles
Frequently asked questions about SOL G.PC.3
What is Virginia SOL G.PC.3?
SOL G.PC.3 is a Geometry Standard of Learning in the Polygons and Circles strand. It expects students to solve problems involving properties of circles.
What skills does SOL G.PC.3 cover?
SOL G.PC.3 is assessed on 6 skills: determine the proportional relationship between the arc length or area of a sector and other parts of a circle; solve for arc measures and angles in a circle formed by central angles; solve for arc measures and angles in a circle involving inscribed angles; calculate the length of an arc of a circle; calculate the area of a sector of a circle; apply arc length or sector area to solve for an unknown measurement of the circle, including the radius, diameter, arc measure, central angle, arc length, or sector area.
What strand of Geometry is SOL G.PC.3 in?
SOL G.PC.3 belongs to the Polygons and Circles reporting strand of the Geometry Virginia Standards of Learning.
How do I study and practice for SOL G.PC.3?
Start with a diagnostic to see whether G.PC.3 is already solid, then work the 6 skills above with guided notes, flashcards, and SOL-style practice questions. For official released items, see the Virginia SOL practice tests guide.