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Quizzes > High School Quizzes > Mathematics

ACT Geometry Practice Quiz

Conquer geometry challenges with clear practice tests

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art promoting the Ace ACT Geometry quiz for high school students.

What is the area of a rectangle with a length of 10 units and a width of 5 units?
15 square units
50 square units
60 square units
40 square units
The area of a rectangle is found by multiplying its length by its width. In this case, 10 multiplied by 5 equals 50 square units.
What is the measure of each angle in an equilateral triangle?
60 degrees
45 degrees
120 degrees
90 degrees
An equilateral triangle has three equal angles, and since the total measure of angles in any triangle is 180°, each angle measures 60°. This is a basic property of equilateral triangles.
What is the measure of a right angle?
60 degrees
45 degrees
90 degrees
180 degrees
A right angle always measures 90 degrees. This is one of the fundamental concepts in geometry.
Which type of angle is greater than 90° but less than 180°?
Right angle
Straight angle
Obtuse angle
Acute angle
An obtuse angle is defined as an angle that is greater than 90° and less than 180°. This distinguishes it from acute, right, and straight angles.
When a transversal cuts through parallel lines, which pair of angles are congruent?
Alternate interior angles
Corresponding angles sum to 90°
Vertical angles
Interior angles are supplementary
When a transversal intersects parallel lines, the alternate interior angles are congruent. This is a key property used in many geometry problems involving parallel lines.
Using the Pythagorean theorem, what is the length of the hypotenuse in a right triangle with legs measuring 6 units and 8 units?
14 units
12 units
10 units
15 units
The Pythagorean theorem states that a² + b² = c². Here, 6² + 8² equals 36 + 64 which is 100, and the square root of 100 is 10 units.
What is the sum of the interior angles in a hexagon?
720 degrees
540 degrees
360 degrees
600 degrees
The sum of the interior angles of an n-sided polygon is calculated by (n-2) - 180°. For a hexagon, where n equals 6, the sum is (6-2) - 180° = 720°.
If the area of a circle is 25π square units, what is its radius?
5 units
25 units
12.5 units
50 units
The area of a circle is given by the formula πr². Equating πr² to 25π and solving for r gives r² = 25, so r equals 5 units.
What is the measure of an exterior angle of a regular pentagon?
90 degrees
60 degrees
108 degrees
72 degrees
An exterior angle of a regular polygon is determined by dividing 360° by the number of sides. For a pentagon, this gives 360° ÷ 5 = 72°.
In a parallelogram, which pair of angles is always congruent?
Interior and exterior angles
Adjacent angles
Opposite angles
Diagonal angles
Opposite angles in a parallelogram are always congruent. This is a defining property of parallelograms and is often used to solve for unknown angles.
What is the distance between the points (1, 2) and (4, 6)?
4 units
√17 units
7 units
5 units
The distance between two points can be found using the distance formula √[(x2 - x1)² + (y2 - y1)²]. Here, it calculates as √[(4-1)²+(6-2)²] = √(9+16) = √25 = 5 units.
A circle has a central angle of 120°. What fraction of the circle does this angle represent?
1/4
1/2
1/3
2/3
The fraction of the circle represented by a central angle is determined by dividing the angle by 360°. Thus, 120°/360° simplifies to 1/3 of the circle.
What is the area of a trapezoid with bases of 10 and 7 units and a height of 5 units?
50 square units
85 square units
42.5 square units
35 square units
The area of a trapezoid is calculated using the formula ((base1 + base2) / 2) - height. Substituting the given values yields ((10 + 7) / 2) - 5 = 42.5 square units.
Find the volume of a cylinder with a radius of 3 units and a height of 10 units.
30π cubic units
90π cubic units
100π cubic units
60π cubic units
The volume of a cylinder is given by the formula πr²h. With a radius of 3 units and a height of 10 units, the volume calculates as π - 9 - 10 = 90π cubic units.
In triangle ABC, if angle A is 60° and angle B is 80°, what is the measure of angle C?
40°
100°
80°
60°
The sum of the interior angles in a triangle is 180°. Subtracting the measures of angle A (60°) and angle B (80°) from 180° leaves angle C measuring 40°.
The sides of a triangle are in the ratio 3:4:5, and the perimeter is 36 units. What is the length of the longest side?
12 units
18 units
10 units
15 units
The sum of the ratio parts is 3 + 4 + 5 = 12, so each part is 36 divided by 12, which equals 3. Multiplying the largest ratio part (5) by 3 gives 15 units for the longest side.
A circle and a square have the same perimeter. If the circle's radius is r, what is the side length of the square in terms of r?
2πr
(πr)/4
(πr)/2
(2r)/π
The perimeter of the circle is 2πr and that of the square is 4s. Equating these (2πr = 4s) and solving for s yields s = (πr)/2.
Which of the following properties regarding the altitudes of a triangle is true?
All altitudes intersect at a point known as the orthocenter
The altitudes divide the triangle into three congruent triangles
Each altitude bisects the opposite side
Altitudes are always equal in length
In every triangle, the three altitudes are concurrent, meaning they intersect at a single point called the orthocenter. This property holds regardless of the type of triangle.
A square and a regular hexagon have equal areas. What is the relationship between the side length of the square (s) and the side length of the hexagon (h)?
s = h · (2√3)/3
s = h · √2
s = h · (√3)/2
s = h · √(3√3/2)
The area of a square is s², and the area of a regular hexagon is given by (3√3/2)h². Equating these areas results in s² = (3√3/2)h², so taking the square root of both sides gives s = h · √(3√3/2).
In similar triangles, if the ratio of similarity is k, what is the ratio of their areas?
2k
k
√k
k²
For similar figures, the ratio of any two corresponding lengths is k, and the ratio of their areas is the square of the ratio of their corresponding sides, which is k².
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Study Outcomes

  1. Analyze ACT-style geometry problems to identify key concepts and strategies.
  2. Apply geometric theorems and formulas to solve complex problems accurately.
  3. Evaluate the properties of various geometric shapes and their relationships.
  4. Interpret diagrams and visual representations to deduce problem solutions.
  5. Synthesize multiple geometric concepts to approach multifaceted questions.

ACT Geometry Practice Cheat Sheet

  1. Master the Pythagorean Theorem - Embrace the power of right triangles by knowing that a² + b² = c². With this formula, you'll breeze through distance problems and verify right angles like a geometry pro. ACT Math Geometry Guide & Practice
    2. blog.prepscholar.com
  2. Understand Special Right Triangles - Spot 45‑45‑90 and 30‑60‑90 triangles in a flash by memorizing their side‑length ratios (x:x:x√2 and x:x√3:2x). This trick saves you precious time on standardized tests. ACT Math Geometry Guide & Practice
    3. blog.prepscholar.com
  3. Know the Area Formulas - From triangles to circles, have these in your back pocket: ½·base·height, length·width, and πr². With area rules nailed down, you'll tackle any shape with confidence. Polygons on ACT Math: Strategies & Practice
    4. blog.prepscholar.com
  4. Memorize Circumference Formulas - Keep 2πr and πd at your fingertips for anything circular. Whether you're finding perimeters or arc lengths, this quick recall is a lifesaver. ACT Math Circles: Geometry Formulas & Strategies
    5. blog.prepscholar.com
  5. Learn the Equation of a Circle - Recognize (x − h)² + (y − k)² = r² at a glance to pinpoint centers and radii. This formula is your golden ticket in coordinate geometry questions. Coordinate Geometry Formulas You Must Know for the ACT
    6. dummies.com
  6. Parallel Lines & Transversals - Alternate interior and corresponding angles are congruent; consecutive interior angles add to 180°. Master these relationships to slice through line problems effortlessly. ACT Math Formulas
    7. testprepservices.princetonreview.com
  7. Sum of Interior Angles in Polygons - Use (n - 2)×180° to find the total degrees inside any n‑sided shape. It's a quick way to tackle weird polygons and angle‑chasing puzzles. Polygons on ACT Math: Strategies & Practice
    8. blog.prepscholar.com
  8. Practice the Midpoint Formula - Split the distance perfectly with ((x₝+x₂)/2, (y₝+y₂)/2). Whether you're bisecting segments or checking centers, this one's indispensable. Coordinate Geometry Formulas You Must Know for the ACT
    9. dummies.com
  9. Apply the Distance Formula - √[(x₂ - x₝)² + (y₂ - y₝)²] gives you the straight‑line distance between any two points. It's like using a ruler digitally - perfect for coordinate challenges. Coordinate Geometry Formulas You Must Know for the ACT
    10. dummies.com
  10. Remember the Slope Formula - (y₂ - y₝)/(x₂ - x₝) reveals how steep a line climbs or falls. With this in hand, graphing and comparing lines becomes a total breeze. Coordinate Geometry Formulas You Must Know for the ACT
    11. dummies.com
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