Geometry · Triangles

Virginia SOL G.TR.4

Virginia SOL G.TR.4 is part of the Triangles strand in Geometry (Math). Under this Standards of Learning objective, students model and solve problems involving right triangle trigonometry and the Pythagorean Theorem. Below is what G.TR.4 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice G.TR.4 for the Virginia SOL test.

Practice G.TR.4 All Geometry standards

What SOL G.TR.4 means

Model and solve problems involving right triangle trigonometry and the Pythagorean Theorem.

Practice Geometry SOL questions

Free Geometry questions from official Virginia Department of Education released SOL tests — good practice while you work on G.TR.4 and the rest of the course. Pick an answer to check it instantly, or open “Show answer” to review.

1. In a circle, m∠CAB = 40°. What is m∠CDB?
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Answer: B — 40°
2. AB is tangent to circle C at B. AB = 15 cm, and the radius of the circle is 8 cm. To the nearest tenth of a centimeter, what is the length of AC?
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Answer: H — 17.0 cm
3. A stained-glass window is in the shape of a semicircle with a radius of 8 ft. Ignoring seams, how much glass is needed?
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Answer: B — 8π sq ft
4. The cargo space of a truck is 2.44 m wide, 2.76 m high, and 8.20 m long. How many cubic meters of cargo space does the truck have?
Show answer
Answer: B — 55.22

→ Take the full free Geometry SOL practice test

Skills you’ll practice for G.TR.4

Determine whether a triangle formed with three given lengths is a right triangle.
Find and verify trigonometric ratios using right triangles.
Model and solve problems, including those in context, involving right triangle trigonometry (sine, cosine, and tangent ratios).
Solve problems using the properties of special right triangles (45°-45°-90° and 30°-60°-90°).
Solve for missing lengths in geometric figures using properties of 45°-45°-90° and 30°-60°-90° triangles, including rationalizing denominators.
Solve problems, including those in context, involving right triangles using the Pythagorean Theorem and its converse, including recognizing Pythagorean Triples.

Key concepts covered by G.TR.4

right triangle
Pythagorean Theorem
triangle formation
trigonometric ratios
right triangles
sine
cosine
tangent
right triangle trigonometry
problem-solving
contextual problems
special right triangles
45°-45°-90°
30°-60°-90°
missing lengths
rationalizing denominators
converse
Pythagorean Triples

How to study and practice SOL G.TR.4

Start with a quick diagnostic to see whether G.TR.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.

→ Take the free Geometry SOL practice test

G.TR.1 — Determine relationships between angles and sides in triangles and solve related problems.
G.TR.2 — Prove and justify triangle congruence using direct and indirect proofs.
G.TR.3 — Prove and justify triangle similarity and solve related problems.

Frequently asked questions about SOL G.TR.4

What is Virginia SOL G.TR.4?

SOL G.TR.4 is a Geometry Standard of Learning in the Triangles strand. It expects students to model and solve problems involving right triangle trigonometry and the Pythagorean Theorem.

What skills does SOL G.TR.4 cover?

SOL G.TR.4 is assessed on 6 skills: determine whether a triangle formed with three given lengths is a right triangle; find and verify trigonometric ratios using right triangles; model and solve problems, including those in context, involving right triangle trigonometry (sine, cosine, and tangent ratios); solve problems using the properties of special right triangles (45°-45°-90° and 30°-60°-90°); solve for missing lengths in geometric figures using properties of 45°-45°-90° and 30°-60°-90° triangles, including rationalizing denominators; solve problems, including those in context, involving right triangles using the Pythagorean Theorem and its converse, including recognizing Pythagorean Triples.

What strand of Geometry is SOL G.TR.4 in?

SOL G.TR.4 belongs to the Triangles reporting strand of the Geometry Virginia Standards of Learning.

How do I study and practice for SOL G.TR.4?

Start with a diagnostic to see whether G.TR.4 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.