TCAP High School (EOC courses) Geometry Practice

TCAP High School (EOC courses) Geometry. Practice it free.

Prove theorems about lines and angles, triangles, circles, and similarity; connect geometric and algebraic reasoning; and solve problems with geometric measurement and coordinate geometry. This High School (EOC courses) reporting domain maps to 14 practice skills and 8 representative questions from the playable bank.

High School (EOC courses)14 mapped skills

Geometry skills

HSG.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment

HSG.CO.2 Represent transformations as functions

HSG.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself

HSG.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments

HSG.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure

HSG.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict and describe the effect of a given rigid motion on a given figure

HSG.CO.7 Use the definition of congruence in terms of rigid motions

HSG.CO.8 Explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions

HSG.CO.9 Prove theorems about lines and angles, triangles, circles, parallelograms, and other figures

HSG.SRT.1 Verify experimentally the properties of dilations

HSG.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar

HSG.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar

HSG.SRT.4 Prove theorems about triangles

HSG.SRT.5 Use congruence and similarity criteria for triangles to solve problems and prove relationships in geometric figures

HSG.C.A.1 Prove that all circles are similar

HSG.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords

HSG.C.A.3 Construct the inscribed and circumscribed circles of a triangle

HSG.C.B.4 Construct a tangent line from a point outside a given circle to the circle

HSG.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem

HSG.GPE.2 Derive the equation of a parabola given a focus and directrix

HSG.GPE.3 Derive the equations of ellipses and hyperbolas given their foci

HSG.GPE.4 Use coordinates to prove simple geometric theorems algebraically

HSG.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

HSG.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio

HSG.GMD.1 Give an informal argument for the formulas for the circumference, area, and volume of geometric figures

HSG.GMD.2 Give an informal argument for the relationship between the measures of the circumference and area of a circle

HSG.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems

HSG.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects

HSG.MG.1 Use geometric shapes, their measures, and their properties to describe objects

HSG.MG.2 Apply concepts of density based on area and volume in modeling situations

HSG.MG.3 Apply geometric methods to solve design problems

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

8 free questions · 0/0 correct

Practice playeasy

Find the volume of a sphere with radius $3$ . Use $\pi = 3$ .

$V = \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \times 3 \times 27 = 108$ .

Practice playeasy

Two parallel lines are cut by a transversal. Same-side interior angles measure $(6x-5)°$ and $(4x+15)°$ . What is the value of $x$ ?

Same-side interior angles are supplementary: $(6x-5)+(4x+15)=180$ , so $10x+10=180$ and $x=17$ .

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(-6, -5)$ and $(-6, 9)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $x$ -coordinate, so the diameter is vertical with length $|9 - (-5)| = 14\textsf{.}$ The radius is half the diameter, so $r = \dfrac{14}{2} = 7\textsf{.}$

Practice playeasy

The equation $x^2 + (y - 6)^2 = 64$ represents Circle A. Circle B is obtained by shifting Circle A down $6$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(0, 6)$ and radius $8$ . Shifting down $6$ moves the center to the origin, so Circle B is $x^2 + y^2 = 64$ .

Practice playeasy

The graph of the equation $(x - 4)^2 + (y + 5)^2 = 36$ 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 $(4, -5)$ and the radius is $6\textsf{.}$ A point on the circle must satisfy $4 - 6 \le a \le 4 + 6\textsf{,}$ so $-2 \le a \le 10\textsf{.}$ The value $3$ is in this interval.

Practice playeasy

Identify the conic: $\dfrac{x^{2}}{16} - \dfrac{y^{2}}{9} = 1$ .

One squared term is subtracted from the other: this is a hyperbola.

Practice playeasy

Riverside has a population density of $1{,}250$ people per square mile and an area of $48$ square miles. What is the population of Riverside?

Set up the proportion $\dfrac{1{,}250\text{ people}}{1\text{ square mile}} = \dfrac{x\text{ people}}{48\text{ square miles}}\textsf{.}$ Cross-multiplying gives $x = 1{,}250 \times 48 = 60{,}000\text{ people}\textsf{.}$

Practice playeasy

A circle in the coordinate plane is centered at the origin and passes through the point $(6, 8)\textsf{.}$ Which equation represents the circle?

The radius is the distance from $(0, 0)$ to $(6, 8)\textsf{:}$ $\sqrt{6^2 + 8^2} = \sqrt{100} = 10$ units. Standard form is $(x - h)^2 + (y - k)^2 = r^2\textsf{,}$ so $x^2 + y^2 = 10^2 = 100\textsf{.}$

Geometry skills

HSG.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment

HSG.CO.2 Represent transformations as functions

HSG.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself

HSG.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments

HSG.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure

HSG.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict and describe the effect of a given rigid motion on a given figure

HSG.CO.7 Use the definition of congruence in terms of rigid motions

HSG.CO.8 Explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions

HSG.CO.9 Prove theorems about lines and angles, triangles, circles, parallelograms, and other figures

HSG.SRT.1 Verify experimentally the properties of dilations

HSG.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar

HSG.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar

HSG.SRT.4 Prove theorems about triangles

HSG.SRT.5 Use congruence and similarity criteria for triangles to solve problems and prove relationships in geometric figures

HSG.C.A.1 Prove that all circles are similar

HSG.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords

HSG.C.A.3 Construct the inscribed and circumscribed circles of a triangle

HSG.C.B.4 Construct a tangent line from a point outside a given circle to the circle

HSG.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem

HSG.GPE.2 Derive the equation of a parabola given a focus and directrix

HSG.GPE.3 Derive the equations of ellipses and hyperbolas given their foci

HSG.GPE.4 Use coordinates to prove simple geometric theorems algebraically

HSG.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

HSG.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio

HSG.GMD.1 Give an informal argument for the formulas for the circumference, area, and volume of geometric figures

HSG.GMD.2 Give an informal argument for the relationship between the measures of the circumference and area of a circle

HSG.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems

HSG.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects

HSG.MG.1 Use geometric shapes, their measures, and their properties to describe objects

HSG.MG.2 Apply concepts of density based on area and volume in modeling situations

HSG.MG.3 Apply geometric methods to solve design problems

Topics mapped to this domain

Surface area and volume

Algebra and polygon angle measures (ACT)

Circle diameter endpoints to radius (SAT)

Circle equation translations (ACT/SAT/PSAT 8/9/10)

Possible coordinates on a circle (SAT)

Conic sections

Density from area and volume

Equation of a circle

Geometric reasoning

Midpoint formula

Parallel and perpendicular lines through a point (SAT)

Parallel and perpendicular slopes from slope-intercept form

8 free questions · 0/0 correct

Turn geometry into game time.

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