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 4 practice skills and 8 representative questions from the playable bank.

Algebra IG-SRT4 mapped skills
What the test measures

Similarity, Right Triangles, and Trigonometry skills

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

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

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

  4. G-SRT.B.4 Prove theorems about triangles

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

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

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

  8. 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.

Practice by skill

Topics mapped to this domain

Geometric reasoning

Grade 910 questions

Right triangle trig from two ratios

Grade 1010 questions

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

Grade 810 questions

Special right triangles

Grade 1015 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

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

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

Practice playeasy

In a right triangle, sin⁡α=725\sin\alpha = \dfrac{7}{25} and cos⁡α=2425\cos\alpha = \dfrac{24}{25}. What is tan⁡α\tan\alpha?

tan⁡α=sin⁡αcos⁡α=7252425=725⋅2524=724\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 77-foot-tall basketball hoop casts a shadow 1414 feet long. At the same time, a brick chimney casts a shadow 2020 feet long. How tall is the chimney, in feet?

Set up 714=h20\dfrac{7}{14} = \dfrac{h}{20}. Cross-multiply: 14h=14014h = 140, so h=10h = 10 feet.

Practice playeasy

In a 3030-6060-9090 triangle the short leg is 33. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×3=62 \times 3 = 6.

Practice playeasy

Two similar triangles have perimeters in the ratio 3:53 : 5. The shortest side of the smaller triangle is 66. 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 3:53 : 5 means each side of the larger triangle is 53\dfrac{5}{3} times the matching side of the smaller. The larger shortest side is 6⋅53=106 \cdot \dfrac{5}{3} = 10.

Practice playeasy

In a right triangle, sin⁡θ=1213\sin\theta = \dfrac{12}{13} and tan⁡θ=125\tan\theta = \dfrac{12}{5}. What is cos⁡θ\cos\theta?

cos⁡θ=sin⁡θtan⁡θ=1213125=1213⋅512=513\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 44 feet tall casts a shadow 55 feet long. A building casts a shadow 6565 feet long at the same time. How tall is the building, in feet?

Set up 45=h65\dfrac{4}{5} = \dfrac{h}{65}. Cross-multiply: 5h=2605h = 260, so h=52h = 52 feet.

Practice playeasy

In a 4545-4545-9090 triangle one leg is 1515. What is the other leg?

Both legs of a 4545-4545-9090 triangle are equal, so the other leg is 1515.

Keep practicing

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

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

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSG.SRT.C.6HSG.SRT.C.8
Similarity, Right Triangles, and Trigonometry in other NJSLA grades
GeometryAlgebra II
Source and test overview
All NJSLA prepOfficial test source
Reporting categories

More Algebra I domains

The Real Number SystemExtend the properties of exponents to rational exponents and use properties of radicals and integer exponents.8 QsPractice →QuantitiesReason quantitatively and use units to solve problems.8 QsPractice →Seeing Structure in ExpressionsInterpret the structure of expressions and write expressions in equivalent forms to solve problems.8 QsPractice →Arithmetic with Polynomials and Rational ExpressionsPerform arithmetic operations on polynomials and understand the relationship between zeros and factors.8 QsPractice →Creating EquationsCreate equations that describe numbers or relationships.8 QsPractice →Reasoning with Equations and InequalitiesUnderstand solving equations as a process of reasoning and explain the reasoning; solve equations and inequalities in one variable; solve systems of equations; represent and solve equations and inequalities graphically.8 QsPractice →