NH SAS Grade 8 Geometry Practice — Sports Academy Games

What the test measures

Geometry skills

Understand congruence and similarity using physical models, transparencies, or geometry software
Understand and apply the Pythagorean theorem
Solve problems involving volume of cylinders, cones, and spheres
Use transformations to analyze and solve problems

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / New Hampshire mathematics standards — New Hampshire

How the NH SAS reports it

New Hampshire SAS is the state assessment system, but the official math reporting structure was not accessible from the state page in this session. In practice, New Hampshire’s math assessments are aligned to the state’s K-12 mathematics standards, which closely mirror Common Core grade-level domains and clusters.

Blueprint & weighting

Not published in the accessible source set used here.

Official sources

New Hampshire Department of Education – Assessments
Common Core State Standards for Mathematics
CCSS-M Grade 3 (Oregon ODE reprint)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

A rectangular prism has length $2$ , width $4$ , and height $9$ . What is its volume?

$V = 2 \times 4 \times 9 = 72$ .

Practice playeasy

Two legs of a right triangle measure $6$ and $8$ . What is the hypotenuse?

$\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$ .

Practice playeasy

In $\triangle XYZ$ , $\angle X$ and $\angle Z$ are congruent. The measure of $\angle Y$ is $52.6^{\circ}$ . What is the measure of $\angle X$ ?

The two congruent angles share the remainder equally: $\dfrac{180^{\circ} - 52.6^{\circ}}{2} = 63.7^{\circ}$ .

Practice playeasy

What is the sum of the interior angles of a pentagon?

A pentagon has $5$ sides: $(5-2) \times 180 = 540°$ .

Practice playeasy

If a right triangle has a hypotenuse of $30$ yards and one leg of $18$ yards, what is the other leg?

Let the missing leg be $x$ . Then $x^{2} + 18^{2} = 30^{2}$ , so $x^{2} = 30^{2} - 18^{2} = 900 - 324 = 576$ and $x = \sqrt{576} = 24$ .

Practice playeasy

A right triangle has legs $20$ and $21$ . What is the hypotenuse?

$20^{2} + 21^{2} = 400 + 441 = 841$ , so the hypotenuse is $\sqrt{841} = 29\textsf{.}$

Practice playeasy

Jordan walks $8$ blocks east and then $15$ blocks north. How many blocks from the starting point is Jordan, measured in a straight line?

The walk forms the legs of a right triangle: $\sqrt{8^{2} + 15^{2}} = \sqrt{64 + 225} = \sqrt{289} = 17$ blocks.

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 $15$ : $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}$