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

NAEP Grade 12 Measurement and Geometry Practice

What the test measures

Measurement and Geometry skills

measurement processes
area and volume
geometric properties
trigonometry-related geometry
conic sections reference
interest rates in applied settings
combinations and permutations reference
mathematical reasoning

Standards basis

NAEP Mathematics Framework (National Assessment Governing Board framework; not a CCSS-M/state standards test blueprint) — national

How the NAEP reports it

NAEP mathematics is organized by the National Assessment Governing Board’s framework, not by state standards. The current framework assesses Grades 4, 8, and 12 and uses five content areas, with item distributions and complexity levels specified in the official framework; it is a national assessment and not aligned to Common Core as a governing blueprint, though it reflects broadly modern school math expectations.

Blueprint & weighting

Published item distribution by grade and content area: Grade 4 — Number Properties and Operations 40%, Measurement 20%, Geometry 15%, Data Analysis/Statistics/Probability 10%, Algebra 15%; Grade 8 — Number Properties and Operations 20%, Measurement 15%, Geometry 20%, Data Analysis/Statistics/Probability 15%, Algebra 30%; Grade 12 — Number Properties and Operations 10%, Measurement and Geometry 30%, Data Analysis/Statistics/Probability 25%, Algebra 35%.

Official sources

National Center for Education Statistics
National Center for Education Statistics
National Center for Education Statistics

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

Find the volume of a cone with radius $3$ and height $5$ . Use $\pi = 3$ .

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 9 \times 5 = 45$ .

Practice playeasy

A culvert pipe is a right circular cylinder with an inside diameter of $12$ inches and a length of $20$ inches. What is the volume of the pipe's interior, in cubic inches?

The radius is $6$ inches. $V = \pi r^{2} h = \pi (6)^{2}(20) = 720\pi$ cubic inches.

Practice playeasy

A fair lists $8$ booths, and a student will visit $2$ of them. What is $C(8, 2)\textsf{?}$

$C(8,2) = \dfrac{8!}{2! \cdot 6!} = \dfrac{40320}{2 \cdot 720} = 28\textsf{.}$

Practice playeasy

A class has $6$ students, and $3$ will speak first, second, and third. What is $P(6, 3)\textsf{?}$

$P(6,3) = \dfrac{6!}{3!} = \dfrac{720}{6} = 120\textsf{.}$

Practice playeasy

What is $6!\textsf{?}$

$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720\textsf{.}$

Practice playeasy

Two parallel lines are cut by a transversal. A pair of corresponding angles measure $(3x+16)°$ and $(2x+34)°$ . What is the measure of each of these angles?

Corresponding angles are congruent: $3x+16=2x+34$ , so $x=18$ . Each angle measures $3(18)+16=70°$ .

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

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?