NY State Math Geometry Similarity, Right Triangles, & Trigonometry Practice

What the test measures

Similarity, Right Triangles, & Trigonometry skills

Understand similarity in terms of similarity transformations
Prove theorems involving similarity
Define trigonometric ratios and solve problems involving right triangles
Apply Trigonometry to general triangles

Standards basis

New York State Learning Standards / New York State Next Generation Learning Standards (NGLS) — New York

How the NY State Math reports it

New York’s Grades 3–8 math tests and Regents math exams are state-developed assessments rather than a shared national framework. The grades 3–8 exams are aligned to New York State learning standards, and the Regents math sequence includes Algebra I, Geometry, and Algebra II, with the June 2026 Algebra II exam explicitly based on the New York State Next Generation Learning Standards.

Blueprint & weighting

Grades 3–8: the official page and the retrieved administration guide describe item/credit structure and timing, but no published domain-by-domain blueprint weighting was located in the primary sources used here. Regents (high school): NYSED publishes a per-conceptual-category 'percent of test by credit' blueprint for each course in its Educator Guides. Algebra I — Number & Quantity 4%–10%, Algebra 48%–61%, Functions 24%–32%, Statistics & Probability 7%–15%. Geometry (single conceptual category, by domain) — Congruence (G-CO) 27%–34%, Similarity, Right Triangles, & Trigonometry (G-SRT) 29%–37%, Circles (G-C) 2%–8%, Expressing Geometric Properties with Equations (G-GPE) 12%–18%, Geometric Measurement & Dimensions (G-GMD) 2%–8%, Modeling with Geometry (G-MG) 8%–15%. Algebra II — Number & Quantity 4%–8%, Algebra 30%–39%, Functions 38%–45%, Statistics & Probability 14%–22%.

Official sources

NYSED Grades 3–8 ELA and Math Test Manuals
NYSED Directions for Administering Regents Examinations
NYSED High School Regents Examinations

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

In a $30°$ - $60°$ - $90°$ triangle, the hypotenuse is $14$ . What is the short leg?

The short leg is half the hypotenuse: $\dfrac{14}{2} = 7$ .

Practice playeasy

In the standard coordinate plane, how many points are both $5$ units from the origin and also exactly $3$ units from the line $x = 0$ ?

Points $5$ units from the origin satisfy $x^{2} + y^{2} = 25$ . Being exactly $3$ units from $x = 0$ means $|x| = 3$ , so $x = 3$ or $x = -3$ . Substituting gives $y^{2} = 16$ , so $y = 4$ or $y = -4$ for each $x$ -value. That yields $(3, 4)$ , $(3, -4)$ , $(-3, 4)$ , and $(-3, -4)$ : $4$ points.

Practice playmedium

A bush that is $2$ feet tall casts a shadow $5$ feet long. At the same time, a cell tower casts a shadow $90$ feet long. How tall is the cell tower, in feet?

Use $\dfrac{2}{5} = \dfrac{h}{90}$ . Cross-multiply: $5h = 180$ , so $h = 36$ feet.

Practice playeasy

In a right triangle, $\sin\alpha = \dfrac{4}{5}$ and $\tan\alpha = \dfrac{4}{3}$ . What is $\cos\alpha$ ?

$\cos\alpha = \dfrac{\sin\alpha}{\tan\alpha} = \dfrac{\dfrac{4}{5}}{\dfrac{4}{3}} = \dfrac{4}{5} \cdot \dfrac{3}{4} = \dfrac{3}{5}$ .

Practice playeasy

In a $30$ - $60$ - $90$ triangle the hypotenuse is $14$ . What is the short leg?

The short leg is half the hypotenuse: $\dfrac{14}{2} = 7$ .

Practice playeasy

In a $45°$ - $45°$ - $90°$ triangle, the hypotenuse is $8\sqrt{2}$ . What is each leg?

Each leg $= \dfrac{\text{hypotenuse}}{\sqrt{2}} = \dfrac{8\sqrt{2}}{\sqrt{2}} = 8$ .

Practice playeasy

Parallel lines $m$ and $n$ are cut by a transversal. At one intersection, an angle measures $115^{\circ}$ . What is the measure of the corresponding angle at the other intersection?

When parallel lines are cut by a transversal, corresponding angles are congruent. The corresponding angle at the second intersection also measures $115^{\circ}$ .

Practice playeasy

A $3$ -foot fence post casts a shadow $2$ feet long. At the same time, a telephone pole casts a shadow $28$ feet long. How tall is the telephone pole, in feet?