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

FAST Geometry EOC Fractional Reasoning Practice

Fractional Reasoning skills

MA.912.FR.1.1, MA.912.FR.1.2

MA.912.G.1.1, MA.912.G.1.2, MA.912.G.1.3

Standards basis

Florida B.E.S.T. Standards — Florida

How the FAST reports it

Florida’s FAST Mathematics is a state-specific assessment program aligned to the Florida B.E.S.T. Standards rather than a national framework. The published blueprint organizes results by reporting categories derived from B.E.S.T. domains, with separate blueprints for grades 3-8 FAST Mathematics and the B.E.S.T. Algebra 1 and Geometry EOCs.

Blueprint & weighting

Florida publishes blueprint percentage ranges by reporting category. The 2025-26 fact sheet states each PM event is tied to a blueprint for the full grade-level content, and the test design summary gives approximate item ranges per reporting category; the reporting-category statements note that a minimum of 15% of raw score points should come from each reporting category, with some domains combined when needed.

Official sources

Florida Department of Education FAST Assessments page
Florida Department of Education B.E.S.T. Mathematics Reporting Category Statements
Florida Department of Education B.E.S.T. Mathematics Test Design Summary

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

A parking meter that is $5$ feet tall casts a shadow $2$ feet long. A radio antenna casts a shadow at the same time. If the antenna is $35$ feet tall, how long is its shadow, in feet?

Use $\dfrac{5}{2} = \dfrac{35}{s}$ . Cross-multiply: $5s = 70$ , so $s = 14$ feet.

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

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

Parallel lines $m$ and $n$ are cut by a transversal. At one intersection, an angle measures $115^{\circ}$ . What is the measure of the corresponding angle at the other intersection?

When parallel lines are cut by a transversal, corresponding angles are congruent. The corresponding angle at the second intersection also measures $115^{\circ}$ .

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 $\triangle ABC$ , the exterior angle at vertex $C$ measures $130^{\circ}$ . If $m\angle A = 48^{\circ}$ , what is $m\angle B$ ?

An exterior angle equals the sum of the two remote interior angles: $m\angle A + m\angle B = 130^{\circ}$ . So $m\angle B = 130^{\circ} - 48^{\circ} = 82^{\circ}$ .

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?