NJSLA Algebra I Similarity, Right Triangles, and Trigonometry Practice

NJSLA Algebra I Similarity, Right Triangles, and Trigonometry. Practice it free.

Understand similarity in terms of similarity transformations; prove theorems involving similarity; define trigonometric ratios and solve problems involving right triangles. This Algebra I reporting domain maps to 5 practice skills and 8 representative questions from the playable bank.

Algebra IG-SRT5 mapped skills

Similarity, Right Triangles, and Trigonometry skills

G-SRT.A.1 Verify experimentally the properties of dilations

G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar

G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar

G-SRT.B.4 Prove theorems about triangles

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures

G-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle

G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles

G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playeasy

Each exterior angle of a regular polygon measures $30^{\circ}$ . How many sides does the polygon have?

The exterior angles of any convex polygon sum to $360^{\circ}$ . For a regular polygon, $n \cdot 30^{\circ} = 360^{\circ}$ , so $n = 12$ .

Practice playeasy

In a right triangle, $\sin\alpha = \dfrac{7}{25}$ and $\cos\alpha = \dfrac{24}{25}$ . What is $\tan\alpha$ ?

$\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha} = \dfrac{\dfrac{7}{25}}{\dfrac{24}{25}} = \dfrac{7}{25} \cdot \dfrac{25}{24} = \dfrac{7}{24}$ .

Practice playeasy

A $7$ -foot-tall basketball hoop casts a shadow $14$ feet long. At the same time, a brick chimney casts a shadow $20$ feet long. How tall is the chimney, in feet?

Set up $\dfrac{7}{14} = \dfrac{h}{20}$ . Cross-multiply: $14h = 140$ , so $h = 10$ feet.

Practice playeasy

In a $30^{\circ}$ - $60^{\circ}$ - $90^{\circ}$ triangle, the hypotenuse is $16\textsf{.}$ What is the short leg?

In a $30^{\circ}$ - $60^{\circ}$ - $90^{\circ}$ triangle, the short leg is half the hypotenuse: $\dfrac{16}{2} = 8\textsf{.}$

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $7$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $7$ .

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, $\sin\theta = \dfrac{12}{13}$ and $\tan\theta = \dfrac{12}{5}$ . What is $\cos\theta$ ?

$\cos\theta = \dfrac{\sin\theta}{\tan\theta} = \dfrac{\dfrac{12}{13}}{\dfrac{12}{5}} = \dfrac{12}{13} \cdot \dfrac{5}{12} = \dfrac{5}{13}$ .

Practice playmedium

A student who is $4$ feet tall casts a shadow $5$ feet long. A building casts a shadow $65$ feet long at the same time. How tall is the building, in feet?

Set up $\dfrac{4}{5} = \dfrac{h}{65}$ . Cross-multiply: $5h = 260$ , so $h = 52$ feet.

NJSLA Algebra I Similarity, Right Triangles, and Trigonometry. Practice it free.

Similarity, Right Triangles, and Trigonometry skills

G-SRT.A.1 Verify experimentally the properties of dilations

G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar

G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar

G-SRT.B.4 Prove theorems about triangles

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures

G-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle

G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles

G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

Topics mapped to this domain

Geometric reasoning

Right triangle trig from two ratios

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

Special right triangle sides (ACT)

Special right triangles

8 free questions · 0/0 correct

Turn similarity, right triangles, and trigonometry into game time.

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