PSSA Grade 8 Geometry. Practice it free.

Measures congruence, similarity, the Pythagorean theorem, transformations, and volume. This Grade 8 reporting domain maps to 9 practice skills and 8 representative questions from the playable bank.

Grade 8M.8.49 mapped skills
What the test measures

Geometry skills

  1. Understand congruence and similarity using physical models, transparencies, or geometry software

  2. Understand and apply the Pythagorean theorem

  3. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

  4. Use rigid transformations to determine congruence and dilation to determine similarity

  5. Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems

Standards basis

Pennsylvania Academic Standards for Mathematics / Pennsylvania Assessment Anchors and Eligible Content — Pennsylvania

How the PSSA reports it

PSSA is Pennsylvania’s own standards-based, criterion-referenced assessment. Its math reporting structure is built on the Pennsylvania Academic Standards/Assessment Anchors and Eligible Content rather than a separate multi-state framework, and it closely mirrors CCSS-style grade-level domains.

Blueprint & weighting

The official PSSA page lists the Mathematics Test Design and grade-level item/scoring samplers, but the accessible source excerpt did not expose a usable per-domain percentage blueprint; no reliable item-weight table was recoverable from the available primary page text.

Try it now

8 free questions · 0/0 correct

Practice playeasy

A right triangle has leg lengths 1616 ft and 3030 ft. Find the length of the hypotenuse.

The legs are 1616 and 3030. By the Pythagorean theorem, 162+302=256+900=1,15616^{2} + 30^{2} = 256 + 900 = 1{,}156, so the hypotenuse is 1,156=34\sqrt{1{,}156} = 34.

Practice playeasy

In a right triangle, the legs have lengths 99 and 1212. What is the length of the hypotenuse?

92+122=81+144=2259^{2} + 12^{2} = 81 + 144 = 225, so the hypotenuse is 225=15.\sqrt{225} = 15\textsf{.}

Practice playeasy

A kite string is 2525 meters long and is staked 77 meters from a point on the ground directly below the kite. How high is the kite?

The string is the hypotenuse: 25272=62549=57625^{2} - 7^{2} = 625 - 49 = 576, so the height is 576=24\sqrt{576} = 24 meters.

Practice playhard

A rectangle has length 88 centimeters and area 120120 square centimeters. What is the length of a diagonal of the rectangle, in centimeters?

Area A=wA = \ell w, so 120=8w120 = 8w and w=15w = 15. The diagonal is the hypotenuse of a right triangle with legs 88 and 1515: 82+152=64+225=289=17 cm.\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}

Practice playeasy

A cylinder has radius 22 and height 44. Using π=3\pi = 3, what is its volume?

V=πr2h=3×4×4=48V = \pi r^2 h = 3 \times 4 \times 4 = 48.

Practice playeasy

What is the length of the vertical segment from (5,3)(5, -3) to (5,9)(5, 9)?

Both points have x=5x = 5, so the length is 9(3)=12|9 - (-3)| = 12.

Practice playmedium

In LMN\triangle LMN, L\angle L and N\angle N are congruent. Each of these angles measures 38.238.2^{\circ}. What is the measure of M\angle M?

Together the congruent angles measure 2×38.2=76.42 \times 38.2^{\circ} = 76.4^{\circ}, so M=18076.4=103.6\angle M = 180^{\circ} - 76.4^{\circ} = 103.6^{\circ}.

Practice playeasy

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

The interior angle sum of a quadrilateral is 360°360°.

Keep practicing

Turn geometry into game time.

The PSSA placement starts with this test's real coverage map and finds the right difficulty.