SOL Geometry Triangles and Quadrilaterals Practice

Triangles and Quadrilaterals skills

triangle congruence and similarity

special quadrilaterals and polygons

right triangles and trigonometric relationships

geometric proofs

Standards basis

Virginia Mathematics Standards of Learning — Virginia

How the SOL reports it

Virginia SOL math is a state-specific assessment program built around the Virginia Mathematics Standards of Learning rather than a shared national test framework. It is aligned to Virginia grade-level and course standards, which are generally CCSS-like in organization but are published as Virginia-specific standards.

Blueprint & weighting

SOL uses the Independent / state-specific framework (by grade domains structure).

Official sources

Virginia Department of Education
VDOE — Standards of Learning for Mathematics (2023 SOL grade/course standards and assessment blueprints)
VDOE — SOL Test Blueprints (per-reporting-category item counts live inside the individual grade/EOC blueprint PDFs)

8 free questions · 0/0 correct

Practice playeasy

Parallel lines $m$ and $n$ are cut by a transversal. At one intersection, an angle measures $115^{\circ}$ . What is the measure of the corresponding angle at the other intersection?

When parallel lines are cut by a transversal, corresponding angles are congruent. The corresponding angle at the second intersection also measures $115^{\circ}$ .

Practice playeasy

A parking meter that is $5$ feet tall casts a shadow $2$ feet long. A radio antenna casts a shadow at the same time. If the antenna is $35$ feet tall, how long is its shadow, in feet?

Use $\dfrac{5}{2} = \dfrac{35}{s}$ . Cross-multiply: $5s = 70$ , so $s = 14$ feet.

Practice playmedium

The graph of the equation $(x + 2)^2 + (y - 15)^2 = 196$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a\textsf{?}$

The center is $(-2, 15)$ and the radius is $14\textsf{.}$ A point on the circle must satisfy $-2 - 14 \le a \le -2 + 14\textsf{,}$ so $-16 \le a \le 12\textsf{.}$ The value $-5$ is in this interval.

Practice playeasy

In a right triangle, $\sin\alpha = \dfrac{5}{13}$ and $\tan\alpha = \dfrac{5}{12}$ . What is $\cos\alpha$ ?

$\cos\alpha = \dfrac{\sin\alpha}{\tan\alpha} = \dfrac{\dfrac{5}{13}}{\dfrac{5}{12}} = \dfrac{5}{13} \cdot \dfrac{12}{5} = \dfrac{12}{13}$ , or from the $5$ - $12$ - $13$ triangle: adjacent $12$ , hypotenuse $13$ .

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $12$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $12$ .

Practice playeasy

In $\triangle ABC$ , the exterior angle at vertex $C$ measures $130^{\circ}$ . If $m\angle A = 48^{\circ}$ , what is $m\angle B$ ?

An exterior angle equals the sum of the two remote interior angles: $m\angle A + m\angle B = 130^{\circ}$ . So $m\angle B = 130^{\circ} - 48^{\circ} = 82^{\circ}$ .

Practice playeasy

A $7$ -foot-tall basketball hoop casts a shadow $14$ feet long. At the same time, a brick chimney casts a shadow $20$ feet long. How tall is the chimney, in feet?

Set up $\dfrac{7}{14} = \dfrac{h}{20}$ . Cross-multiply: $14h = 140$ , so $h = 10$ feet.

Practice playeasy

The graph of the equation $(x - 7)^2 + (y - 3)^2 = 25$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a\textsf{?}$

The center is $(7, 3)$ and the radius is $5\textsf{.}$ A point on the circle must satisfy $7 - 5 \le a \le 7 + 5\textsf{,}$ so $2 \le a \le 12\textsf{.}$ The value $9$ is in this interval.