VTCAP Grade 9 Geometry Practice — Sports Academy Games

VTCAP Grade 9 Geometry. Practice it free.

High school geometry content reported as the 'Geometry' performance indicator; blueprint target: 9-13 points (20-29% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus areas listed below (congruence, transformations, constructions, and coordinate arguments with slope, distance, perimeter, and area). This Grade 9 reporting domain maps to 6 practice skills and 8 representative questions from the playable bank.

Grade 96 mapped skills

Geometry skills

Congruence

Express Geometric Properties with Equations

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — Vermont

How the VTCAP reports it

Vermont administered the Smarter Balanced summative through spring 2022, then replaced it with the Cognia-developed Vermont Comprehensive Assessment Program (VTCAP) beginning spring 2023 — this landing slug predates the switch. VTCAP mathematics is an adaptive, CCSS-M-aligned assessment in grades 3-9. It is NOT a Smarter Balanced administration: its reporting categories are groupings of the CCSS grade-level domains (e.g. 'The Number System, Expressions and Equations'), not SBAC claims, though two cross-grade Mathematical Practices indicators ('Problem Solving, Reasoning, and Argument'; 'Modeling, Patterns, and Structure') echo the old claim structure. Per the test specifications, the grades 3-8 test may assess any CCSS-M standard at the grade; the grade 9 test assesses a prioritized subset of the high school CCSS-M within the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability (the assessed focus areas are published in the grade 9 Performance Level Descriptors).

Blueprint & weighting

VTCAP Test Specifications (Spring 2026) operational test blueprint, target percent of points per grade — Grade 3: OA 24-35%, NBT 10-14%, NF 16-20%, MD 22-29%, G 6-10%, constructed-response Mathematical Practices 12%. Grade 4: OA 20-31%, NBT 16-20%, NF 20-31%, MD 12-20%, G 6-10%, practices 12%. Grade 5: OA 14-22%, NBT 14-25%, NF 22-29%, MD 20-27%, G 8-16%, practices 12%. Grade 6: RP 15-22%, NS 15-22%, EE 15-22%, G 11-19%, SP 11-19%, practices 11%. Grade 7: RP 15-22%, NS 11%, EE 15-30%, G 11-19%, SP 19-22%, practices 11%. Grade 8: F 18-29%, NS 7%, EE 20-31%, G 18-29%, SP 18-22%, practices 11%. Grade 9 (all machine-scored): Number and Quantity/Algebra 18-27%, Algebra/Functions 31-40%, Geometry 20-29%, Statistics and Probability 13-20%; the two practices indicators are dual-aligned targets of >18% of points each. Identical figures appear in the Spring 2025 specifications.

Official sources

VTCAP Test Specifications, Spring 2026 (Vermont AOE / Cognia)
VTCAP Test Specifications, Spring 2025 (Vermont AOE / Cognia)
VTCAP Performance Level Descriptors: Mathematics, Grades 3-9 (Vermont AOE)

8 free questions · 0/0 correct

Practice playeasy

In parallelogram $PQRS$ , $m\angle P=(4x+6)°$ and $m\angle Q=(2x+24)°$ . What is the measure of $\angle P$ ?

Consecutive angles are supplementary: $(4x+6)+(2x+24)=180$ , so $6x+30=180$ and $x=25$ . Then $m\angle P=4(25)+6=106°$ .

Practice playeasy

Which transformation creates an image that is congruent to its preimage, but is located at a different angle around a center point?

A rotation is a rigid transformation that turns a figure around a fixed point, called a center of rotation, by a specific angle in a specific direction. All points remain equidistant from the center of rotation, keeping the image congruent to the preimage. In this example, the image is congruent to the preimage and is located at a different angle around that center point.

Practice playmedium

The graph of the equation $(x + 1)^2 + (y + 10)^2 = 144$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a\textsf{?}$

The center is $(-1, -10)$ and the radius is $12\textsf{.}$ A point on the circle must satisfy $-1 - 12 \le a \le -1 + 12\textsf{,}$ so $-13 \le a \le 11\textsf{.}$ The value $6$ is in this interval.

Practice playeasy

Find the midpoint of $(0, 10)$ and $(8, 2)$ . What is the $x$ -coordinate?

$x$ -coordinate $= \dfrac{0 + 8}{2} = \dfrac{8}{2} = 4$ .

Practice playmedium

The equation of a line is $y = \dfrac{1}{3}x + 4$ . Which equation represents the line that is perpendicular to this line and passes through the point $(3, 2)$ ?

Perpendicular lines have slopes that are negative reciprocals, so $m = -3$ . Substitute $(3, 2)$ into $y = -3x + b$ : $2 = -3(3) + b = -9 + b$ , so $b = 11$ . The equation is $y = -3x + 11\textsf{.}$

Practice playeasy

Line $u$ is defined by $y = \dfrac{2}{5}x - 3$ . Line $v$ is perpendicular to line $u$ in the coordinate plane. What is the slope of line $v$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $u$ is $\dfrac{2}{5}$ , so the slope of line $v$ is $-\dfrac{5}{2}\textsf{.}$

Practice playeasy

Each interior angle of rectangle $WXYZ$ measures $(3x-12)°$ . What is the value of $x$ ?

Every interior angle of a rectangle measures $90°$ , so $3x-12=90$ and $x=34$ .

Practice playeasy

Which transformation never keeps a point in the same place?

A translation is a rigid transformation that moves every point of a figure the exact same distance in the same direction. Since all points in the image remain equidistant from the points in the preimage, the figure remains congruent. In this example, a point is never kept in the same place.