Ohio State Tests Geometry Similarity and Trigonometry Practice

Ohio State Tests Geometry Similarity and Trigonometry. Practice it free.

Ohio's State Test Geometry end-of-course math subscore covering similarity, right triangles, and trigonometry, plus geometric measurement and modeling — similarity transformations, right-triangle trigonometry, volume formulas, and applying geometric concepts in modeling (Ohio's Learning Standards high-school Geometry conceptual category, Similarity/Right Triangles & Trigonometry, Geometric Measurement & Dimension, and Modeling with Geometry). This Geometry reporting domain maps to 7 practice skills and 8 representative questions from the playable bank.

Geometry7 mapped skills

Similarity and Trigonometry skills

Understand similarity and prove theorems involving similarity, define and apply right-triangle trigonometry, explain and use volume formulas, and apply geometric concepts in modeling situations

Standards basis

Ohio's Learning Standards (mathematics) — Common Core-derived (CCSS-M) — Ohio

How the Ohio State Tests reports it

Ohio's State Tests are Ohio-specific assessments built around Ohio's Learning Standards for Mathematics, which are CCSS-derived and retain the Common Core grade-level domains and (at high school) conceptual categories nearly verbatim. Math is tested in grades 3-8 and via end-of-course exams; the high-school graduation pathway uses Algebra I and Geometry, but students in an integrated sequence take Integrated Mathematics I and II in their place (these integrated courses are not given their own bands here — Integrated Math I draws on the same Algebra/Functions/Number & Quantity/Geometry/Statistics content as Algebra I plus early Geometry, and Integrated Math II adds the remaining Geometry/Functions/Probability content). The reporting categories below are the official math subscore categories Ohio publishes per test; because no public item-percentage blueprint was retrievable, the cluster-level Common Core domains those subscores cover are used (the standards' grade-level domains, which the reporting categories mirror).

Blueprint & weighting

Ohio publishes per-test math subscore (reporting) categories in its Subscore Definitions chart and raw-score subscale ranges, but no public per-category item-percentage blueprint was retrievable; the statistical summaries report the number of items per subscore by administration rather than a fixed blueprint weighting.

Official sources

Ohio Department of Education and Workforce — Ohio's State Tests Subscore Definitions (OSTSubscoreChart.pdf)
Ohio Department of Education and Workforce — Ohio's State Tests Spring 2025 Statistical Summary
Ohio Department of Education and Workforce — Ohio's State Tests in ELA, Mathematics, Science and Social Studies

8 free questions · 0/0 correct

Practice playeasy

Find the surface area of a sphere with radius $1$ . Use $\pi = 3$ .

$SA = 4 \pi r^{2} = 4 \times 3 \times 1 = 12$ .

Practice playeasy

A city park has a density of $35$ picnic tables per acre and covers $24$ acres. How many picnic tables are in the park?

Set up the proportion $\dfrac{35\text{ picnic tables}}{1\text{ acre}} = \dfrac{x\text{ picnic tables}}{24\text{ acres}}\textsf{.}$ Cross-multiplying gives $x = 35 \times 24 = 840\text{ picnic tables}\textsf{.}$

Practice playeasy

Two similar triangles have perimeters in the ratio $3 : 5$ . The shortest side of the smaller triangle is $6$ . What is the length of the shortest side of the larger triangle if corresponding sides are compared?

Similar figures have a constant scale factor between corresponding lengths. Perimeter ratio $3 : 5$ means each side of the larger triangle is $\dfrac{5}{3}$ times the matching side of the smaller. The larger shortest side is $6 \cdot \dfrac{5}{3} = 10$ .

Practice playeasy

In a right triangle, $\sin\alpha = \dfrac{5}{13}$ and $\tan\alpha = \dfrac{5}{12}$ . What is $\cos\alpha$ ?

$\cos\alpha = \dfrac{\sin\alpha}{\tan\alpha} = \dfrac{\dfrac{5}{13}}{\dfrac{5}{12}} = \dfrac{5}{13} \cdot \dfrac{12}{5} = \dfrac{12}{13}$ , or from the $5$ - $12$ - $13$ triangle: adjacent $12$ , hypotenuse $13$ .

Practice playeasy

A parking meter that is $5$ feet tall casts a shadow $2$ feet long. A radio antenna casts a shadow at the same time. If the antenna is $35$ feet tall, how long is its shadow, in feet?

Use $\dfrac{5}{2} = \dfrac{35}{s}$ . Cross-multiply: $5s = 70$ , so $s = 14$ feet.

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $12$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $12$ .

Practice playhard

A concrete drainage pipe is a hollow right circular cylinder. The outer radius is $r_1 = 6$ meters, the inner radius is $r_2 = 4$ meters, and the pipe is $5$ meters long. What is the volume of concrete in the pipe wall, in cubic meters?

Wall volume is outer minus inner: $V = \pi h(r_1^{2} - r_2^{2}) = \pi (5)(6^{2} - 4^{2}) = \pi (5)(20) = 100\pi$ cubic meters.

Practice playeasy

Find the volume of a cylinder with radius $1$ and height $10$ . Use $\pi = 3$ .

$V = \pi r^2 h = 3 \times 1 \times 10 = 30$ .

Ohio State Tests Geometry Similarity and Trigonometry. Practice it free.

Similarity and Trigonometry skills

Understand similarity and prove theorems involving similarity, define and apply right-triangle trigonometry, explain and use volume formulas, and apply geometric concepts in modeling situations

Topics mapped to this domain

Surface area and volume

Density from area and volume

Geometric reasoning

Right triangle trig from two ratios

Similar triangle shadows (ACT/SAT/PSAT 8/9/10)

Special right triangles

Volume word problems (ACT)

8 free questions · 0/0 correct

Turn similarity and trigonometry into game time.

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