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 5 practice skills and 8 representative questions from the playable bank.

Grade 95 mapped skills
What the test measures

Geometry skills

  1. Congruence

  2. 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.

Practice by skill

Topics mapped to this domain

Algebra and polygon angle measures (ACT)

Grade 910 questions

Possible coordinates on a circle (SAT)

Grade 1010 questions

Midpoint formula

Grade 1015 questions

Parallel and perpendicular lines through a point (SAT)

Grade 910 questions

Parallel and perpendicular slopes from slope-intercept form

Grade 910 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

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

Consecutive angles are supplementary: (4x+6)+(2x+24)=180(4x+6)+(2x+24)=180, so 6x+30=1806x+30=180 and x=25x=25. Then m∠P=4(25)+6=106°m\angle P=4(25)+6=106°.

Practice playmedium

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

The center is (−1,−10)(-1, -10) and the radius is 12.12\textsf{.} A point on the circle must satisfy −1−12≤a≤−1+12,-1 - 12 \le a \le -1 + 12\textsf{,} so −13≤a≤11.-13 \le a \le 11\textsf{.} The value 66 is in this interval.

Practice playeasy

Point M(5,4)M(5, 4) is the midpoint of a segment with one endpoint at (2,1)(2, 1). What is the xx-coordinate of the other endpoint?

Since 2+x2=5\dfrac{2 + x}{2} = 5, we get x=10−2=8x = 10 - 2 = 8.

Practice playmedium

The equation of a line is y=13x+4y = \dfrac{1}{3}x + 4. Which equation represents the line that is perpendicular to this line and passes through the point (3,2)(3, 2)?

Perpendicular lines have slopes that are negative reciprocals, so m=−3m = -3. Substitute (3,2)(3, 2) into y=−3x+by = -3x + b: 2=−3(3)+b=−9+b2 = -3(3) + b = -9 + b, so b=11b = 11. The equation is y=−3x+11.y = -3x + 11\textsf{.}

Practice playeasy

Line uu is defined by y=25x−3y = \dfrac{2}{5}x - 3. Line vv is perpendicular to line uu in the coordinate plane. What is the slope of line vv?

Perpendicular lines have slopes that are negative reciprocals. The slope of line uu is 25\dfrac{2}{5}, so the slope of line vv is −52.-\dfrac{5}{2}\textsf{.}

Practice playeasy

Each interior angle of rectangle WXYZWXYZ measures (3x−12)°(3x-12)°. What is the value of xx?

Every interior angle of a rectangle measures 90°90°, so 3x−12=903x-12=90 and x=34x=34.

Practice playmedium

The graph of the equation (x+8)2+(y−6)2=169(x + 8)^2 + (y - 6)^2 = 169 is a circle in the coordinate plane. The point (a,b)(a, b) lies on the circle. Which of the following is a possible value for b?b\textsf{?}

The center is (−8,6)(-8, 6) and the radius is 13.13\textsf{.} A point on the circle must satisfy 6−13≤b≤6+13,6 - 13 \le b \le 6 + 13\textsf{,} so −7≤b≤19.-7 \le b \le 19\textsf{.} The value 1111 is in this interval.

Practice playeasy

Find the midpoint of (4,6)(4, 6) and (10,2)(10, 2). What is the xx-coordinate?

xx-coordinate =4+102=142=7= \dfrac{4 + 10}{2} = \dfrac{14}{2} = 7.

Keep practicing

Turn geometry into game time.

The VTCAP placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSG.GPE.B.6
Geometry in other VTCAP grades
Grade 5Grade 6Grade 7Grade 8
Source and test overview
All VTCAP prepOfficial test source
Reporting categories

More Grade 9 domains

Number and Quantity/AlgebraHigh school number/quantity and algebra content reported as the 'Number and Quantity/Algebra' performance indicator; blueprint target: 8-12 points (18-27% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus areas listed below; they are placed under this slash-named category by their CCSS conceptual category (Number and Quantity, Algebra).8 QsPractice →Algebra/FunctionsHigh school function content reported as the 'Algebra/Functions' performance indicator; blueprint target: 14-18 points (31-40% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus areas listed below; they are placed under this slash-named category by their CCSS conceptual category (Functions, spanning linear, quadratic, and exponential function algebra).8 QsPractice →Statistics and ProbabilityHigh school statistics content reported as the 'Statistics and Probability' performance indicator; blueprint target: 6-10 points (13-20% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus area listed below (one-variable displays, center and spread, two-way tables, scatterplots, fitted functions, correlation, and causation).8 QsPractice →