Grade 8 Math · Measurement and Geometry
Virginia SOL 8.MG.4
Virginia SOL 8.MG.4 is part of the Measurement and Geometry strand in Grade 8 Math (Math). Under this Standards of Learning objective, students apply the Pythagorean Theorem to solve problems involving right triangles. Below is what 8.MG.4 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice 8.MG.4 for the Virginia SOL test.
What SOL 8.MG.4 means
Apply the Pythagorean Theorem to solve problems involving right triangles.
Practice Grade 8 Math SOL questions
Free Grade 8 Math questions from official Virginia Department of Education released SOL tests — good practice while you work on 8.MG.4 and the rest of the course. Pick an answer to check it instantly, or open “Show answer” to review.
1. Billy must paint the surface area of a square-based pyramid. The base is a square with side length 7 inches. Each triangular face has a base of 7 inches and a slant height of 15 inches. What is the total surface area?
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Answer: J — 175 sq in.
2. A bookshelf has a triangular brace connecting two points that are 20 inches apart horizontally and 15 inches apart vertically. Which is closest to the length of the brace?
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Answer: A — 25 in.
3. A pizza parlor offers: 4 sizes (small, medium, large, extra large) 3 crust types (thin, original, thick) 4 toppings How many ways can Andy buy a pizza with one topping?
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Answer: B — 4 × 3 × 4
4. The highest January temperatures (°F) for 10 U.S. cities are: 37, 38, 39, 42, 42, 46, 47, 53, 54, 60 In how many cities was the highest January temperature above 45°F?
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Answer: B — 5
Skills you’ll practice for 8.MG.4
- Verify the Pythagorean Theorem using diagrams, concrete materials, and measurement.
- Determine whether a triangle is a right triangle given the measures of its three sides.
- Identify the hypotenuse and legs of a right triangle given figures in various orientations.
- Determine the measure of a side of a right triangle given the measures of the other two sides.
- Apply the Pythagorean Theorem and its converse to solve problems involving right triangles in context.
Key concepts covered by 8.MG.4
- Pythagorean Theorem
- verification
- diagrams
- concrete materials
- measurement
- right triangle
- side measures
- hypotenuse
- legs
- figure orientation
- side measure
- converse
- contextual problems
How to study and practice SOL 8.MG.4
Start with a quick diagnostic to see whether 8.MG.4 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 Grade 8 Math standards in Measurement and Geometry
- 8.MG.1 — Use relationships among vertical, adjacent, supplementary, and complementary angles to determine unknown angle measures.
- 8.MG.2 — Determine surface area of square-based pyramids and volume of cones and square-based pyramids.
- 8.MG.3 — Apply translations and reflections to polygons in the coordinate plane.
- 8.MG.5 — Solve area and perimeter problems involving composite plane figures.
Frequently asked questions about SOL 8.MG.4
What is Virginia SOL 8.MG.4?
SOL 8.MG.4 is a Grade 8 Math Standard of Learning in the Measurement and Geometry strand. It expects students to apply the Pythagorean Theorem to solve problems involving right triangles.
What skills does SOL 8.MG.4 cover?
SOL 8.MG.4 is assessed on 5 skills: verify the Pythagorean Theorem using diagrams, concrete materials, and measurement; determine whether a triangle is a right triangle given the measures of its three sides; identify the hypotenuse and legs of a right triangle given figures in various orientations; determine the measure of a side of a right triangle given the measures of the other two sides; apply the Pythagorean Theorem and its converse to solve problems involving right triangles in context.
What strand of Grade 8 Math is SOL 8.MG.4 in?
SOL 8.MG.4 belongs to the Measurement and Geometry reporting strand of the Grade 8 Math Virginia Standards of Learning.
How do I study and practice for SOL 8.MG.4?
Start with a diagnostic to see whether 8.MG.4 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.