Geometry · Polygons and Circles
Virginia SOL G.PC.1
Virginia SOL G.PC.1 is part of the Polygons and Circles strand in Geometry (Math). Under this Standards of Learning objective, students prove and justify theorems and properties of quadrilaterals and solve related problems. Below is what G.PC.1 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice G.PC.1 for the Virginia SOL test.
What SOL G.PC.1 means
Prove and justify theorems and properties of quadrilaterals and solve related problems.
Practice Geometry SOL questions
Free Geometry questions from official Virginia Department of Education released SOL tests — good practice while you work on G.PC.1 and the rest of the course. Pick an answer to check it instantly, or open “Show answer” to review.
1. What is the approximate volume of a can that is 5 inches tall and has a 2.5-inch diameter?
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Answer: G — 24.5 cu in.
2. A rectangular prism tank measures 40 cm by 20 cm. The water level rises 0.4 cm when a rock is submerged. What is the volume of the rock?
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Answer: A — 320 cm³
3. The ratio between the volumes of two spheres is 27 to 8. What is the ratio between their radii?
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Answer: J — 3:2
4. A surveyor measures distances of 12 ft and 9 ft along one bank of a river and 52 ft along the opposite bank. Which is a good estimate of the distance across the river?
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Answer: C — 40 ft
Skills you’ll practice for G.PC.1
- Solve problems using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, and trapezoids.
- Prove and justify that quadrilaterals have specific properties using coordinate and algebraic methods, such as the slope formula, the distance formula, and the midpoint formula.
- Prove and justify theorems and properties of quadrilaterals using deductive reasoning.
- Use congruent segment, congruent angle, angle bisector, perpendicular line, and/or parallel line constructions to verify properties of quadrilaterals.
Key concepts covered by G.PC.1
- quadrilaterals
- parallelograms
- rectangles
- rhombi
- squares
- isosceles trapezoids
- trapezoids
- problem-solving
- quadrilateral properties
- coordinate methods
- slope formula
- distance formula
- midpoint formula
- proofs
- quadrilateral theorems
- deductive reasoning
- geometric constructions
- congruent segments
- congruent angles
- angle bisectors
- perpendicular lines
- parallel lines
How to study and practice SOL G.PC.1
Start with a quick diagnostic to see whether G.PC.1 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.1
What is Virginia SOL G.PC.1?
SOL G.PC.1 is a Geometry Standard of Learning in the Polygons and Circles strand. It expects students to prove and justify theorems and properties of quadrilaterals and solve related problems.
What skills does SOL G.PC.1 cover?
SOL G.PC.1 is assessed on 4 skills: solve problems using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, and trapezoids; prove and justify that quadrilaterals have specific properties using coordinate and algebraic methods, such as the slope formula, the distance formula, and the midpoint formula; prove and justify theorems and properties of quadrilaterals using deductive reasoning; use congruent segment, congruent angle, angle bisector, perpendicular line, and/or parallel line constructions to verify properties of quadrilaterals.
What strand of Geometry is SOL G.PC.1 in?
SOL G.PC.1 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.1?
Start with a diagnostic to see whether G.PC.1 is already solid, then work the 4 skills above with guided notes, flashcards, and SOL-style practice questions. For official released items, see the Virginia SOL practice tests guide.