KAP Grade 8 Geometry. Practice it free.

Uses similarity, the Pythagorean theorem, and volume to solve geometric problems. 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

  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. Solve problems involving angle relationships and transformations

  5. Use informal arguments to establish facts about angle sum and parallel lines

Standards basis

Kansas College and Career Ready Standards for Mathematics (CCRS-M), closely aligned to Common Core State Standards for Mathematics (CCSS-M) — Kansas

How the KAP reports it

Kansas Assessment Program appears to be a state assessment program rather than a vendor framework like Smarter Balanced or PARCC. The public KAP site did not expose a math blueprint or reporting-category document in the pages I could access, so the safest official mapping is to the state's adopted mathematics standards structure that the assessment is built to.

Blueprint & weighting

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

Practice by skill

Topics mapped to this domain

Isosceles triangle angles

Grade 810 questions

Polygon angle formulas

Grade 815 questions

Triangle angle sum

Grade 810 questions

Volume of prisms and cylinders

Grade 731 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 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

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 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 KAP 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
8.G.A.57.G.B.68.G.C.98.G.B.88.G.B.7
Geometry in other KAP grades
Grade 4Grade 5Grade 6Grade 7
The same skills on other tests
i-ReadyNAEPAASAACAP
Source and test overview
All KAP prepOfficial test source
Reporting categories

More Grade 8 domains

The Number SystemWorks with irrational numbers and exponents, and understands properties of integer exponents and scientific notation.8 QsPractice →Expressions and EquationsAnalyzes and solves linear equations, systems, and relationships using algebraic reasoning.8 QsPractice →FunctionsDefines, evaluates, and compares functions, and uses functions to model relationships.8 QsPractice →Statistics and ProbabilityInvestigates patterns of association in bivariate data and summarizes data distributions.8 QsPractice →