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Quizzes > High School Quizzes > Mathematics

Geometry EOC Practice Test

Solve EOC geometry questions for exam success

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting Geometry EOC Challenge trivia for high school students.

What is a polygon?
An open figure composed of several lines
A three-dimensional shape with flat faces
A figure with curved sides and no angles
A closed plane figure with at least three straight sides and angles
A polygon is defined as a closed figure consisting entirely of straight line segments. This definition requires a minimum of three sides and angles to form a closed shape.
Which angle is defined as a right angle?
90° angle
360° angle
180° angle
45° angle
A right angle is one that measures exactly 90°. This is a fundamental concept in geometry used to establish perpendicularity.
What is the sum of the interior angles in a triangle?
270°
180°
360°
90°
The interior angles of any triangle sum to 180°. This property is a cornerstone of Euclidean geometry.
Which of the following best describes an isosceles triangle?
A triangle with three equal sides
A triangle with two equal sides
A triangle with all different side lengths
A triangle with one right angle
An isosceles triangle is characterized by having at least two sides of equal length. This feature also typically results in two equal base angles.
What is the Pythagorean theorem?
a² + b² = c²
a² + b² = ab
2a + 2b = c
a + b = c
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. This theorem is fundamental in various geometric calculations.
Which of the following is true about supplementary angles?
They add up to 270°
They add up to 180°
They add up to 360°
They add up to 90°
Supplementary angles are those whose measures add up to 180°. This concept is often used to solve problems involving linear pairs or adjacent angles.
For a circle with radius r, what is the formula for its area?
πr
2πr²
2πr
πr²
The area of a circle is calculated using the formula πr². This formula derives from the relationship between the radius and the circle's curvature.
What is the relationship between the side lengths of similar triangles?
They have no relation
They are proportional
They are arranged in an arithmetic progression
They are always equal
Similar triangles have corresponding sides that are proportional. This consistent ratio between sides is a key property used in solving problems involving similar figures.
What is the measure of each interior angle of a regular hexagon?
100°
90°
144°
120°
A regular hexagon has six equal interior angles. Using the formula (n - 2) × 180°/n, where n = 6, each angle measures 120°.
If two angles in a triangle measure 50° and 60°, what is the measure of the third angle?
100°
70°
90°
80°
The sum of the angles in a triangle is always 180°. Subtracting the sum of 50° and 60° from 180° leaves 70° for the third angle.
Which of the following properties is true for an equilateral triangle?
It has two equal sides only
It has three different angles
All sides and angles are equal
It has one 90° angle
An equilateral triangle has all three sides and all three angles equal. Each angle in an equilateral triangle measures 60°.
What is the formula for the distance between two points (x₝, y₝) and (x₂, y₂) in a plane?
(x₂ - x₝) * (y₂ - y₝)
√((x₂ - x₝)² - (y₂ - y₝)²)
√((x₂ - x₝)² + (y₂ - y₝)²)
(x₂ - x₝) + (y₂ - y₝)
The distance between two points in the coordinate plane is determined by the Pythagorean theorem, leading to the formula √((x₂ - x₝)² + (y₂ - y₝)²). This formula is essential for solving many geometry and coordinate problems.
What is the circumference of a circle with diameter d?
πd
πd²
2πd
πr²
The circumference of a circle can be expressed as π times the diameter. Since the diameter is twice the radius, this formula is equivalent to 2πr.
If a line is perpendicular to another line, what is the angle between them?
180°
90°
0°
45°
Perpendicular lines intersect to form a right angle, which is exactly 90°. This is a foundational concept used to define perpendicularity in geometry.
In a parallelogram, which of the following statements is true?
Sides are not necessarily equal; angles are always acute
Opposite sides are unequal; adjacent angles are equal
Adjacent sides are equal and angles are always 90°
Opposite sides are equal and parallel; opposite angles are equal
A parallelogram is defined by having opposite sides that are both equal in length and parallel, with opposite angles being equal. This distinguishes it from other quadrilaterals and is key to its geometric properties.
Given a circle with center (h, k) and radius r, what is the standard form of its equation?
(x - h)² + (y - k)² = r²
x² + y² = r²
(x + h)² + (y + k)² = r²
(x - h) + (y - k) = r
The standard form of a circle's equation is (x - h)² + (y - k)² = r². This formula represents a circle centered at (h, k) with a radius of r.
If the lines 3x + 4y = 12 and 6x + 8y = k are parallel, what must k equal?
24
12
36
48
For two lines to be parallel, their coefficients must be proportional. Doubling the equation 3x + 4y = 12 gives 6x + 8y = 24, so k must be 24.
In triangle ABC, if the interior angles are in the ratio 3:4:5, what is the measure of the largest angle?
75°
120°
105°
90°
The ratio of the angles is 3:4:5, which adds up to 12 parts. Since the total measure of a triangle is 180°, each part measures 15° (180°/12). The largest angle, being 5 parts, is 75°.
What is the area of a trapezoid with bases measuring 10 and 14, and a height of 8?
96
112
104
88
The area of a trapezoid is determined by the formula A = ½ × (base1 + base2) × height. Substituting the given values yields A = ½ × (10 + 14) × 8 = 96.
Which statement is true when an altitude is drawn from a vertex to the base in a triangle?
It always lies outside the triangle
It always bisects the base
It divides the triangle into two congruent triangles
It is perpendicular to the base
An altitude in a triangle is defined as the perpendicular segment from a vertex to the line containing the opposite side (the base). This guarantees a right angle where the altitude meets the base.
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Study Outcomes

  1. Understand and apply key geometric postulates and theorems.
  2. Analyze relationships between angles, lines, and shapes.
  3. Calculate measurements such as lengths, angles, and areas in various geometric figures.
  4. Evaluate conditions for congruence and similarity in shapes.
  5. Solve real-world problems using rigorous geometric reasoning and proofs.

Geometry EOC Practice Test Cheat Sheet

  1. Understand angle relationships - Angles are the building blocks of geometry! Get comfy with complementary (sum to 90°), supplementary (sum to 180°), vertical (opposite angles) and adjacent relationships - remember vertical angles are always congruent! EOCT Analytic Geometry Study Guide
    2. studylib.net
  2. Master the Pythagorean Theorem - This classic formula, a² + b² = c², is your ticket to finding missing sides in right triangles. Play around with different a and b values to see how the hypotenuse changes - it's like geometry magic! EOC Best Study Guide
    3. studocu.com
  3. Learn area & perimeter formulas - Whether you're fencing a yard (perimeter) or painting a wall (area), formulas like A = ½ × base × height for triangles and A = πr² for circles will save your day. Memorize and practice so you can apply them without breaking a sweat! Shape Formulas Guide
    4. studocu.com
  4. Explore parallel & perpendicular lines - Lines that never meet (parallel) or hit at right angles (perpendicular) come alive when you add a transversal. Spot alternate interior and corresponding angles to unlock congruence and supplementary pairs like a pro! Transversal Tricks
    5. studylib.net
  5. Study transformations - Slide it (translation), spin it (rotation), flip it (reflection) or resize it (dilation). Rigid moves keep shape and size intact - perfect when you need to prove congruence without lifting a protractor! EOC Transformation Resources
    6. sites.google.com
  6. Review triangle congruence shortcuts - SSS, SAS, ASA, AAS and HL are your five golden keys to proving triangles match up. No need to compare every side and angle - just pick the shortcut that fits the data! Triangle Congruence
    7. studocu.com
  7. Know special quadrilateral properties - Parallelograms, rectangles, rhombuses and squares each have their quirks. For instance, opposite sides of a parallelogram are equal and parallel - spot these traits to classify shapes instantly! Quadrilateral Cheat Sheet
    8. studocu.com
  8. Calculate volume & surface area - From πr²h for cylinders to 4/3·πr³ for spheres, 3D formulas help you determine how much space objects take up. Practice visualizing slices and nets to nail these calculations! 3D Geometry Formulas
    9. studocu.com
  9. Use distance & midpoint formulas - In the coordinate plane, the distance formula √[(x₂ - x₝)² + (y₂ - y₝)²] finds the length between points, while the midpoint formula averages coordinates. They're your dynamic duo for analytic geometry! Coordinate Plane Tools
    10. studocu.com
  10. Grasp basic trigonometry - SOH‑CAH‑TOA is your trusty mnemonic: sine = opp/hyp, cosine = adj/hyp, tangent = opp/adj. Use these ratios to unlock angles and side lengths in any right triangle situation! Trigonometry Quick‑Start
    11. studocu.com
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