ISAT Grade 8 Geometry. Practice it free.

Applies similarity, transformations, and the Pythagorean Theorem. This Grade 8 reporting domain maps to 9 practice skills and 8 representative questions from the playable bank.

Grade 89 mapped skills

What the test measures

Geometry skills

Understand congruence and similarity using physical models, transparencies, or geometry software
Understand and apply the Pythagorean Theorem
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

Standards basis

Idaho Content Standards (Mathematics) — Idaho

How the ISAT reports it

Idaho ISAT is a state assessment administered to grades 3–8 and 11 and reported against Idaho grade-level content standards rather than a separate national testing framework. The public ISAT page points to summative blueprints and math specifications, while the Idaho Content Standards page shows the math program is organized by grade-band/domain progressions aligned to Idaho standards.

Blueprint & weighting

The public Idaho ISAT page references summative blueprints and item specifications, but the accessible official page content did not expose a published domain-by-domain percentage blueprint for math.

Official sources

Idaho Department of Education — Idaho Standards Achievement Test (ISAT)
Idaho Department of Education — Idaho Content Standards

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

A cylinder has radius $1$ and height $5$ . Using $\pi = 3$ , what is its volume?

$V = \pi r^2 h = 3 \times 1 \times 5 = 15$ .

Practice playeasy

What is the distance from $(1, 2)$ to $(4, 6)$ ?

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

Practice playeasy

In $\triangle PQR$ , $\angle P$ and $\angle Q$ are congruent. The measure of $\angle R$ is $118.6^{\circ}$ . What is the measure of $\angle Q$ ?

Let each congruent angle measure $x^{\circ}$ . Then $2x + 118.6 = 180$ , so $x = \dfrac{180 - 118.6}{2} = 30.7^{\circ}$ .

Practice playeasy

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

A octagon has $8$ sides: $(8-2) \times 180 = 1080°$ .

Practice playmedium

The shorter leg of a right triangle is $11$ centimeters and the longer leg is $60$ centimeters. What is the length of the hypotenuse?

The legs are $11$ and $60$ . By the Pythagorean theorem, $11^{2} + 60^{2} = 121 + 3{,}600 = 3{,}721$ , so the hypotenuse is $\sqrt{3{,}721} = 61$ .

Practice playeasy

The hypotenuse of a right triangle is $25$ , and one leg is $7$ . Find the other leg.

$25^{2} - 7^{2} = 625 - 49 = 576$ , so the other leg is $\sqrt{576} = 24\textsf{.}$

Practice playeasy

A kite string is $25$ meters long and is staked $7$ meters from a point on the ground directly below the kite. How high is the kite?

The string is the hypotenuse: $25^{2} - 7^{2} = 625 - 49 = 576$ , so the height is $\sqrt{576} = 24$ meters.

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