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Quizzes > High School Quizzes > Mathematics

Unit 7 Polygons & Quadrilaterals Practice Quiz

Review study guide with test answer key

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art promoting the Polygons and Quads Quiz for high school students.

What is a polygon?
A flat shape with no sides
A line with endpoints
A curved shape with angles
A closed figure with three or more straight sides
A polygon is defined as a closed two-dimensional shape composed of straight line segments connected end-to-end. Option B is correct because it captures the essential features of a polygon.
Which of the following shapes is a quadrilateral?
Triangle
Rectangle
Pentagon
Hexagon
A quadrilateral is a polygon with exactly four sides. A rectangle is a specific type of quadrilateral that has four sides and four right angles, making option C the correct choice.
How many sides does a quadrilateral have?
Four
Five
Six
Three
By definition, a quadrilateral is a four-sided polygon. Therefore, option C, which states that a quadrilateral has four sides, is correct.
Which of the following best describes a regular polygon?
A polygon with no symmetry
A polygon with unequal sides and angles
A polygon with only two equal sides
A polygon with all sides and angles equal
A regular polygon has all sides of equal length and all interior angles equal. This equal distribution of sides and angles ensures high symmetry, making option B the correct answer.
Which of these is NOT a property of all polygons?
They have straight sides
They always have equal side lengths
They are closed shapes
They have interior angles
All polygons are closed shapes with straight sides that form interior angles. However, having equal side lengths is not a required property for a shape to be classified as a polygon, which makes option D the correct answer.
What is the sum of the interior angles of a pentagon?
450 degrees
540 degrees
720 degrees
360 degrees
The formula for the sum of the interior angles of an n-sided polygon is (n-2)*180 degrees. For a pentagon, where n = 5, the sum is (5-2)*180 = 540 degrees, making option A correct.
Which formula correctly calculates the sum of interior angles of a polygon with n sides?
(n-2)*180
n*180
(n+2)*180
(2n-4)*90
The correct formula for the sum of interior angles in any polygon is (n-2)*180 degrees, which breaks the polygon into (n-2) triangles. Option B is correct as it directly applies this formula.
A rectangle has which set of properties?
Only one pair of parallel sides and unequal angles
Opposite sides equal and four right angles
Four congruent sides and no right angles
Four congruent sides and variable angles
A rectangle is defined by having both pairs of opposite sides equal and all four angles as 90 degrees. This definition makes option B the correct description of a rectangle.
Which property is unique to a square compared to a rectangle?
Opposite sides are parallel
Diagonals bisect each other
All angles are 90 degrees
All sides are equal in length
While both squares and rectangles share the property of having four right angles, a square uniquely has all four sides of equal length. Therefore, option A is correct as it distinguishes a square from a rectangle.
Which quadrilateral has only one pair of parallel sides?
Rectangle
Rhombus
Trapezoid
Parallelogram
A trapezoid is defined as a quadrilateral with only one pair of parallel sides, unlike a parallelogram, rectangle, or rhombus which typically have two pairs. This makes option C the correct answer.
How many diagonals does a quadrilateral have?
2
4
3
1
The number of diagonals in any polygon can be calculated using the formula n(n-3)/2. For a quadrilateral (n=4), this becomes 4(4-3)/2 = 2, so option B is correct.
The exterior angle of a regular polygon is given by what formula?
720/n
(n-2)*180/n
360/n
180/n
In any regular polygon, the sum of the exterior angles is always 360 degrees, so each exterior angle measures 360 divided by the number of sides (n). Option A is thus the correct formula.
What distinguishes a parallelogram from other quadrilaterals?
All sides are of equal length
Both pairs of opposite sides are parallel and equal in length
Only one pair of sides is parallel
It has no parallel sides
A parallelogram is characterized by having both pairs of opposite sides that are parallel and equal in length. This specific property sets it apart from other quadrilaterals, making option B correct.
Which of the following is true about the diagonals of a rectangle?
They always intersect at the vertex
They are equal in length and bisect each other
They are unequal and do not bisect each other
They are perpendicular
In a rectangle, the diagonals are congruent (equal in length) and they intersect each other by bisecting one another. Option B accurately describes this important property.
If a regular polygon has 12 sides, what is the measure of each interior angle?
150 degrees
120 degrees
160 degrees
135 degrees
For a regular polygon, the sum of the interior angles is calculated by (n-2)*180 degrees. With 12 sides, the sum is (12-2)*180 = 1800 degrees, and each interior angle is 1800/12 = 150 degrees. Therefore, option B is correct.
A quadrilateral has one pair of parallel sides and the non-parallel sides are equal in length. What is this shape most commonly called?
Isosceles Trapezoid
Kite
Parallelogram
Rhombus
A trapezoid is a quadrilateral with one pair of parallel sides. When the non-parallel sides are equal in length, the shape is specifically called an isosceles trapezoid, which makes option B correct.
Which of the following properties always holds true for the diagonals of a rhombus?
They never intersect
They bisect the vertex angles
They are perpendicular to each other
They are equal in length
A defining property of a rhombus is that its diagonals intersect at right angles, meaning they are perpendicular. This property is constant regardless of the side lengths, so option C is correct.
Given an irregular quadrilateral with interior angles measuring 80°, 95°, and 100°, what is the measure of the fourth angle?
105°
95°
85°
75°
The sum of the interior angles of any quadrilateral is 360°. Adding the given angles (80° + 95° + 100°) gives 275°, and subtracting from 360° results in an 85° angle. Therefore, option B is correct.
In a regular polygon, if each exterior angle measures 30 degrees, how many sides does the polygon have?
12
15
18
10
For a regular polygon, the sum of the exterior angles is always 360°. Dividing 360° by the measure of each exterior angle (30°) gives 12, meaning the polygon has 12 sides. Option B is therefore correct.
Which quadrilateral can have its diagonals both equal in length and perpendicular, and what additional condition must it satisfy?
Kite; it typically has one axis of symmetry
Square; it must have all sides equal and all angles 90°
Rectangle; it only needs to have right angles
Rhombus; it must have all sides equal
A square uniquely combines the characteristics of both a rectangle and a rhombus; its diagonals are equal in length like a rectangle and perpendicular like a rhombus because it has four equal sides and four right angles. This makes option C the correct answer.
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Study Outcomes

  1. Analyze the properties of various polygons including side counts, angles, and symmetry.
  2. Differentiate between various types of quadrilaterals such as squares, rectangles, parallelograms, and trapezoids.
  3. Apply the formulas for perimeter and area to calculate measurements of polygons and quadrilaterals.
  4. Demonstrate problem-solving skills by identifying polygon types based on geometric properties.

Unit 7 Polygons & Quadrilaterals Test Cheat Sheet

  1. Explore Quadrilaterals - Quadrilaterals are four‑sided polygons where all interior angles add up to 360°, so every corner party is perfectly balanced. From kites to trapeziums, they come in loads of fun shapes and sizes. Quick Quadrilateral Guide
    2. geeksforgeeks.org
  2. Master the Seven Types - Get to know the squad: square, rectangle, rhombus, parallelogram, trapezium, isosceles trapezium, and kite - each with its own signature moves. Visualizing their unique properties helps you spot them in real life and ace your geometry quizzes. List of Quadrilateral Types
    3. testbook.com
  3. Learn Area Formulas - Area = side² for squares, length × width for rectangles, and special twists for other shapes. Memorize these core formulas and you'll measure any quadrilateral like a pro. Area Formulas Breakdown
    4. byjus.com
  4. Diagonals Demystified - In parallelograms, diagonals bisect each other, while in rectangles they're equal in length - like perfect mirror images. Play around by drawing a few and see these magical bisectors in action. Diagonals in Quadrilaterals
    5. geeksforgeeks.org
  5. Rhombus Revealed - All four sides of a rhombus are equal, and its diagonals not only bisect each other but also meet at right angles - talk about a precision dance! Sketch one to watch the right angles pop up. Rhombus Properties
    6. geeksforgeeks.org
  6. Trapezium Tricks - A trapezium has one pair of parallel sides, and you calculate its area with ½ × (sum of parallel sides) × height. It's like a trapeze act: balance the two parallels and measure the "drop" between them. Trapezium Area Explainer
    7. geeksforgeeks.org
  7. Kite Shape Fun - Kites have two pairs of adjacent equal sides, and their diagonals intersect at right angles - so they always fly straight in your sketches. Try folding paper kites to see these right‑angle diagonals for yourself. Kite Shape Properties
    8. geeksforgeeks.org
  8. Perimeter Pointers - The perimeter of any quadrilateral is just the sum of its four sides, and special shapes have neat shortcuts, like 4 × side for squares. Counting edges is as simple as a number line hop! Quadrilateral Perimeter Formulas
    9. geeksforgeeks.org
  9. Cyclic Quadrilateral Coolness - If you inscribe a quadrilateral in a circle, its opposite angles always add up to 180° - a perfect semicircle handshake. This circle trick shows up in many contest problems! Cyclic Quadrilaterals Guide
    10. en.wikipedia.org
  10. Bretschneider's Formula - For any quadrilateral, Area = √((s - a)(s - b)(s - c)(s - d) - a b c d × cos²((α+γ)/2)), where s is the semiperimeter - geometry's secret handshake. It's like Brahmagupta's formula on steroids, covering all corner cases! Bretschneider's Formula Explained
    11. en.wikipedia.org
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