WVGSA Grade 8 Geometry Practice — Sports Academy Games

What the test measures

Geometry skills

Verify properties of rigid motions.
Identify and describe congruence and similarity.
Analyze angle relationships and similarity of triangles.
Explain and apply the Pythagorean Theorem.
Find distances in the coordinate plane.
Solve volume problems for cylinders, cones, and spheres.

Standards basis

West Virginia College- and Career-Readiness Standards for Mathematics (WVBE Policy 2520.2B) — West Virginia

How the WVGSA reports it

West Virginia’s General Summative Assessment is a state assessment aligned to the West Virginia College- and Career-Readiness Standards rather than a separate national assessment framework. The math blueprint follows CCSS-style grade-band domains and clusters, but the standards are the state’s own West Virginia College- and Career-Readiness Standards.

Blueprint & weighting

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

Official sources

West Virginia Department of Education: General Summative Assessment
West Virginia Department of Education: Grade 3 Mathematics Standards
West Virginia Department of Education: Grade 4 Mathematics Standards

Practice by skill

Topics mapped to this domain

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8 free questions · 0/0 correct

Practice playeasy

A rectangular prism has length $3$ , width $3$ , and height $5$ . What is its volume?

$V = 3 \times 3 \times 5 = 45$ .

Practice playeasy

What is the distance from $(0, 0)$ to $(3, 4)$ ?

$\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$ .

Practice playeasy

In $\triangle RST$ , $\angle R$ and $\angle T$ are congruent. The measure of each of these angles is $43.9^{\circ}$ . What is the measure of $\angle S$ ?

The congruent angles total $2 \times 43.9^{\circ} = 87.8^{\circ}$ , so $\angle S = 180^{\circ} - 87.8^{\circ} = 92.2^{\circ}$ .

Practice playeasy

What is the sum of the exterior angles, one at each vertex, of any convex polygon?

The exterior angles of any convex polygon, one at each vertex, sum to $360^{\circ}\textsf{.}$

Practice playeasy

The legs of a right triangle are $12$ inches and $35$ inches long. How long is the hypotenuse?

The legs are $12$ and $35$ . By the Pythagorean theorem, $12^{2} + 35^{2} = 144 + 1{,}225 = 1{,}369$ , so the hypotenuse is $\sqrt{1{,}369} = 37$ .

Practice playeasy

A right triangle has legs $8$ and $15$ . What is the hypotenuse?

$8^{2} + 15^{2} = 64 + 225 = 289$ , so the hypotenuse is $\sqrt{289} = 17\textsf{.}$

Practice playeasy

A wheelchair ramp rises $5$ feet over a horizontal distance of $12$ feet. What is the length of the ramp?

The ramp is the hypotenuse of a right triangle with legs $5$ and $12$ : $\sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13$ feet.

Practice playhard

A rectangle has length $8$ centimeters and area $120$ square centimeters. What is the length of a diagonal of the rectangle, in centimeters?

Area $A = \ell w$ , so $120 = 8w$ and $w = 15$ . The diagonal is the hypotenuse of a right triangle with legs $8$ and $15$ : $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}$