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Quizzes > Mathematics

Geometry Quiz: Basic Assessment

Quick, free basic geometry test to check your skills. Instant results.

Editorial: Review CompletedCreated By: Robert DumasUpdated Aug 25, 2025
Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art depicting elements related to Basic Geometry Assessment Quiz

This geometry quiz helps you check your understanding of shapes, angles, and basic formulas, and see where to review. Answer quick multiple-choice questions and get instant feedback with tips. Want more practice? Try the geometry chapter 1 quiz for fundamentals, warm up with some geometry trivia, or prep for bigger exams with the geometry final practice test.

Which shape has three sides and three angles?
Triangle
Pentagon
Rectangle
Square
A triangle is defined as a polygon with three sides and three angles. It is the simplest polygon with exactly three edges and vertices.
What is the perimeter of a rectangle with length 5 units and width 3 units?
8 units
15 units
16 units
10 units
Perimeter of a rectangle equals 2Ã-(length+width) = 2Ã-(5+3) = 16 units. This sums all four sides of the rectangle.
What is the area of a square with side length 4 units?
12 square units
8 square units
4 square units
16 square units
Area of a square is side², so 4² = 16 square units. Each side being equal makes this formula straightforward.
What is the measure of a right angle?
60 degrees
90 degrees
45 degrees
180 degrees
A right angle measures exactly 90 degrees. It is the standard angle formed by perpendicular lines.
What is the sum of the interior angles of any triangle?
270 degrees
360 degrees
90 degrees
180 degrees
The sum of the interior angles in any triangle is always 180 degrees. This is a fundamental property of all triangles.
What is the area of a circle with radius 7 units?
28Ï€ square units
14Ï€ square units
7Ï€ square units
49Ï€ square units
Area of a circle is Ï€r², so Ï€Ã-7² = 49Ï€ square units. The radius squared times Ï€ yields the area.
What is the area of a parallelogram with base 10 units and height 4 units?
20 square units
40 square units
100 square units
14 square units
Area of a parallelogram is base Ã- height = 10 Ã- 4 = 40 square units. Height is the perpendicular distance to the base.
Two angles are complementary if they add up to what sum?
45 degrees
180 degrees
360 degrees
90 degrees
Complementary angles sum to 90 degrees by definition. This distinguishes them from supplementary angles, which sum to 180 degrees.
In a linear pair, if one angle measures 110 degrees, what is the measure of the adjacent angle?
110 degrees
60 degrees
90 degrees
70 degrees
Linear pair angles are supplementary and sum to 180°, so the adjacent angle = 180° - 110° = 70°. They share a common side on a straight line.
What is the perimeter of an equilateral triangle with each side measuring 6 units?
6 units
12 units
18 units
24 units
All sides of an equilateral triangle are equal, so perimeter = 3 Ã- 6 = 18 units. Each side length contributes equally.
What quadrilateral has four equal sides but not necessarily right angles?
Parallelogram
Trapezoid
Rhombus
Rectangle
A rhombus has all four sides equal in length, but its interior angles are not required to be right angles. It is a special parallelogram.
What kind of angle is formed by two perpendicular lines?
Straight angle
Acute angle
Obtuse angle
Right angle
Perpendicular lines intersect to form right angles, each measuring 90 degrees. This is the defining property of perpendicularity.
What is the sum of the interior angles of a convex pentagon?
720 degrees
450 degrees
540 degrees
360 degrees
For any n-sided polygon, the sum of interior angles is (n - 2)Ã-180°. For n=5, 3Ã-180° = 540°.
When two parallel lines are cut by a transversal, corresponding angles are:
Adjacent
Supplementary
Complementary
Equal
Corresponding angles are congruent when lines are parallel and cut by a transversal. They occupy matching positions relative to the lines.
What is the length of the side of a square whose area is 144 square units?
24 units
72 units
12 units
144 units
Since area = side², taking the square root of 144 yields side = 12 units. Only the positive root applies for side lengths.
What is the area of a trapezoid with bases of lengths 8 units and 12 units and a height of 5 units?
100 square units
20 square units
50 square units
40 square units
Area = ((base1 + base2)/2) Ã- height = ((8 + 12)/2) Ã- 5 = 10 Ã- 5 = 50 square units. It uses the average of the bases.
In a triangle, two angles measure 2x and 3x, and the third angle measures 100 degrees. What is the value of x?
80
16
20
10
Sum of angles = 180°, so 2x + 3x + 100 = 180, giving 5x = 80 and x = 16 degrees. This solves the linear equation.
A circle has a circumference of approximately 31.4 units. What is its radius? (Use π ≈ 3.14)
15 units
5 units
10 units
2.5 units
Circumference C = 2Ï€r, so r = C/(2Ï€) = 31.4/(2Ã-3.14) = 31.4/6.28 = 5 units. This uses the definition of circumference.
In a parallelogram, one interior angle measures 70 degrees. What are the measures of the other three angles?
110°, 110°, 110°
70°, 70°, 70°
110°, 70°, 110°
90°, 90°, 90°
Adjacent angles in a parallelogram are supplementary, so they measure 110°. Opposite angles are equal, so the sequence is 70°, 110°, 70°, 110°.
A rectangle has an area of 48 square units and a perimeter of 28 units. What are its length and width?
Length 10 units and width 4.8 units
Length 9 units and width 5 units
Length 8 units and width 6 units
Length 12 units and width 4 units
From L+W=14 and LW=48, solving L(14âˆ'L)=48 yields L=8 and W=6. These satisfy both perimeter and area conditions.
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Learning Outcomes

  1. Master key geometric definitions and properties
  2. Apply formulas to calculate area and perimeter
  3. Identify different types of angles and their measures
  4. Analyse relationships between shapes and angles
  5. Demonstrate problem-solving strategies for geometry tasks

Cheat Sheet

  1. Fundamental Geometric Terms - A line extends infinitely in both directions, while a line segment has defined endpoints. Parallel lines never intersect and perpendicular lines meet at right angles, forming a vertex where two lines meet - master these definitions to tackle any geometry problem with confidence.
  2. Key Area Formulas - Remember that a rectangle's area is length × width, a triangle's is ½ × base × height, and a circle's is π × radius². These formulas are your go-to tools for finding the space contained by shapes in assignments and exams.
  3. Perimeter & Circumference Formulas - The perimeter of a square is 4 × side length and for a rectangle it's 2 × (length + width). The circumference of a circle, its perimeter, is 2 × π × radius; knowing these lets you calculate any boundary length effectively.
  4. Angle Types - Acute angles measure less than 90°, right angles are exactly 90°, obtuse angles range between 90° and 180°, and reflex angles are over 180°. Spotting these quickly will speed up your angle-related problem-solving.
  5. Sum of Interior Angles in Polygons - A triangle's interior angles always total 180°, while a quadrilateral's total 360°. Apply this rule to find unknown angles in any multi-sided figure easily.
  6. Pythagorean Theorem - In right triangles, the square of the hypotenuse equals the sum of the squares of the other sides (a² + b² = c²). Use this to find missing side lengths or check if a triangle is right-angled.
  7. Parallel Line Angle Relationships - When a transversal cuts parallel lines, corresponding angles match and alternate interior angles are equal. These relationships are essential for solving unknown angles quickly.
  8. Triangle Congruence & Similarity - Triangles are congruent if they share equal sides and angles (SSS, SAS, ASA) and similar if their angles match and sides are proportional. Recognizing these helps you prove geometric properties with ease.
  9. Circle Basics - The radius runs from the center to any point on the circle, while the diameter is twice that distance. The circumference is 2 × π × radius, and the area is π × radius² - essential facts for any circle problem.
  10. Problem-Solving Strategies - Break complex problems into smaller steps, sketch diagrams to visualize shapes, and apply geometric rules in order. Regular practice builds confidence and sharpens your geometry skills for tests and real-life scenarios.
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