VTCAP Grade 8 Geometry. Practice it free.

Grade 8 Geometry standards; reported jointly with statistics as the 'Geometry and Statistics and Probability' performance indicator. Blueprint target: 10-16 points (18-29% of the grade 8 test). This Grade 8 reporting domain maps to 9 practice skills and 8 representative questions from the playable bank.

Grade 88.G9 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

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — Vermont

How the VTCAP reports it

Vermont administered the Smarter Balanced summative through spring 2022, then replaced it with the Cognia-developed Vermont Comprehensive Assessment Program (VTCAP) beginning spring 2023 — this landing slug predates the switch. VTCAP mathematics is an adaptive, CCSS-M-aligned assessment in grades 3-9. It is NOT a Smarter Balanced administration: its reporting categories are groupings of the CCSS grade-level domains (e.g. 'The Number System, Expressions and Equations'), not SBAC claims, though two cross-grade Mathematical Practices indicators ('Problem Solving, Reasoning, and Argument'; 'Modeling, Patterns, and Structure') echo the old claim structure. Per the test specifications, the grades 3-8 test may assess any CCSS-M standard at the grade; the grade 9 test assesses a prioritized subset of the high school CCSS-M within the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability (the assessed focus areas are published in the grade 9 Performance Level Descriptors).

Blueprint & weighting

VTCAP Test Specifications (Spring 2026) operational test blueprint, target percent of points per grade — Grade 3: OA 24-35%, NBT 10-14%, NF 16-20%, MD 22-29%, G 6-10%, constructed-response Mathematical Practices 12%. Grade 4: OA 20-31%, NBT 16-20%, NF 20-31%, MD 12-20%, G 6-10%, practices 12%. Grade 5: OA 14-22%, NBT 14-25%, NF 22-29%, MD 20-27%, G 8-16%, practices 12%. Grade 6: RP 15-22%, NS 15-22%, EE 15-22%, G 11-19%, SP 11-19%, practices 11%. Grade 7: RP 15-22%, NS 11%, EE 15-30%, G 11-19%, SP 19-22%, practices 11%. Grade 8: F 18-29%, NS 7%, EE 20-31%, G 18-29%, SP 18-22%, practices 11%. Grade 9 (all machine-scored): Number and Quantity/Algebra 18-27%, Algebra/Functions 31-40%, Geometry 20-29%, Statistics and Probability 13-20%; the two practices indicators are dual-aligned targets of >18% of points each. Identical figures appear in the Spring 2025 specifications.

Practice by skill

Topics mapped to this domain

Volume of prisms and cylinders

Grade 731 questions

Isosceles triangle angles

Grade 810 questions

Polygon angle formulas

Grade 815 questions

Triangle angle sum

Grade 810 questions

Distance formula

Grade 815 questions

Finding a missing side with the Pythagorean theorem

Grade 810 questions

Pythagorean theorem

Grade 811 questions

Pythagorean theorem in context (SAT/ACT)

Grade 86 questions

Rectangle diagonal from area (ACT)

Grade 83 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

A rectangular prism has length 22, width 55, and height 66. What is its volume?

V=2×5×6=60V = 2 \times 5 \times 6 = 60.

Practice playmedium

In △GHI\triangle GHI, ∠G\angle G and ∠I\angle I are congruent. The measure of ∠H\angle H is 88.4∘88.4^{\circ}. What is the measure of ∠G\angle G?

Each congruent angle is 180∘−88.4∘2=45.8∘\dfrac{180^{\circ} - 88.4^{\circ}}{2} = 45.8^{\circ}.

Practice playeasy

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

A nonagon has 99 sides: (9−2)×180=1260°(9-2) \times 180 = 1260°.

Practice playeasy

In △DEF,\triangle DEF\textsf{,} m∠Dm\angle D and m∠Em\angle E together measure 127∘.127^{\circ}\textsf{.} What is m∠F?m\angle F\textsf{?}

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} So m∠F=180∘−127∘=53∘.m\angle F = 180^{\circ} - 127^{\circ} = 53^{\circ}\textsf{.}

Practice playeasy

How long is the segment joining (−1,−5)(-1, -5) and (−1,2)(-1, 2)?

Both points have x=−1x = -1, so the length is ∣2−(−5)∣=7|2 - (-5)| = 7.

Practice playmedium

A right triangle has hypotenuse 3939 inches. One of its legs measures 1515 inches. What is the measure of the remaining leg?

Let the missing leg be xx. Then x2+152=392x^{2} + 15^{2} = 39^{2}, so x2=392−152=1,521−225=1,296x^{2} = 39^{2} - 15^{2} = 1{,}521 - 225 = 1{,}296 and x=1,296=36x = \sqrt{1{,}296} = 36.

Practice playeasy

A right triangle has legs 55 and 1212. What is the hypotenuse?

52+122=25+144=1695^{2} + 12^{2} = 25 + 144 = 169, so the hypotenuse is 169=13.\sqrt{169} = 13\textsf{.}

Practice playeasy

Jordan walks 88 blocks east and then 1515 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: 82+152=64+225=289=17\sqrt{8^{2} + 15^{2}} = \sqrt{64 + 225} = \sqrt{289} = 17 blocks.

Keep practicing

Turn geometry into game time.

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

Batting Cage game coverBatting CagePlay →Blaster Gate game coverBlaster GatePlay →Blitz Tanks game coverBlitz TanksPlay →Buzzer Beater game coverBuzzer BeaterPlay →
Related Common Core standards
7.G.B.68.G.C.98.G.A.58.G.B.88.G.B.7
Geometry in other VTCAP grades
Grade 5Grade 6Grade 7Grade 9
The same skills on other tests
i-ReadyNAEPAASAACAP
Source and test overview
All VTCAP prepOfficial test source
Reporting categories

More Grade 8 domains

FunctionsGrade 8 Functions standards; reported as the 'Functions' performance indicator. Blueprint target: 10-16 points (18-29% of the grade 8 test).8 QsPractice →The Number SystemGrade 8 Number System standards; reported jointly with expressions and equations as 'The Number System, Expressions and Equations' performance indicator. Blueprint target: 4 points (7% of the grade 8 test).8 QsPractice →Expressions and EquationsGrade 8 Expressions and Equations standards; reported jointly with the number system as 'The Number System, Expressions and Equations' performance indicator. Blueprint target: 11-17 points (20-31% of the grade 8 test).8 QsPractice →Statistics and ProbabilityGrade 8 Statistics and Probability standards; reported jointly with geometry as the 'Geometry and Statistics and Probability' performance indicator. Blueprint target: 10-12 points (18-22% of the grade 8 test).8 QsPractice →