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

PARCC Geometry Similarity, Right Triangles, and Trigonometry Practice

Similarity, Right Triangles, and Trigonometry skills

Understand similarity in terms of similarity transformations

Prove theorems involving similarity

Define trigonometric ratios and solve problems involving right triangles

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / PARCC Model Content Frameworks — national

How the PARCC reports it

PARCC was a multistate assessment system built around the Common Core-era PARCC mathematics model content frameworks rather than a separate proprietary standards set. Its math structure is organized by grade/course and aligned to CCSS-M content categories and model content frameworks.

Blueprint & weighting

No single published PARCC weighting table was located in the accessible sources used here.

Official sources

PARCC Assessment
Common Core State Standards Initiative

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, $\sin\alpha = \dfrac{7}{25}$ 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 $30$ - $60$ - $90$ triangle the short leg is $3$ . What is the hypotenuse?

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

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, $\sin\theta = \dfrac{12}{13}$ 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?