In isosceles triangle DEF with DE cong DF, each base angle measures 58°. Which side has the greatest length?

DE and DF are equal and longest

NJSLA Geometry Similarity, Right Triangles, and Trigonometry Practice

NJSLA Geometry 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 Geometry reporting domain maps to 5 practice skills and 8 representative questions from the playable bank.

GeometryG-SRT5 mapped skills

Similarity, Right Triangles, and Trigonometry skills

G.SRT.A.1-3 Similarity transformations and AA criterion

G.SRT.B.4-5 Triangle similarity and proof applications

G.SRT.C.6-8 Trigonometric ratios and right triangle applications

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

In isosceles $\triangle DEF$ with $DE \cong DF$ , each base angle measures $58^{\circ}$ . Which side has the greatest length?

The base angles at $E$ and $F$ each measure $58^{\circ}$ , so the vertex angle at $D$ is $180^{\circ} - 2(58^{\circ}) = 64^{\circ}$ . The greatest angle is at $D$ , so the opposite side $EF$ is the longest.

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.

Practice playeasy

In a $30^{\circ}$ - $60^{\circ}$ - $90^{\circ}$ triangle, the short leg is $10\textsf{.}$ What is the hypotenuse?

In a $30^{\circ}$ - $60^{\circ}$ - $90^{\circ}$ triangle, the hypotenuse is twice the short leg: $2 \times 10 = 20\textsf{.}$

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $15$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $15$ .

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 playeasy

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

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

Practice playmedium

At a zoo, a keeper who is $6$ feet tall casts a shadow $4$ feet long. A giraffe standing nearby casts a shadow at the same time. If the giraffe is $21$ feet tall, how long is its shadow, in feet?