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Quizzes > High School Quizzes > Mathematics

Unit 6 Polygons & Quadrilaterals Practice Quiz

Boost your geometry skills with detailed answers

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting a trivia quiz on polygons and quadrilaterals for 8th-10th graders.

Which of the following shapes is a polygon?
Oval
Ellipse
Circle
Triangle
A polygon is a closed figure with straight sides. A triangle, having three straight sides, fits this definition.
How many sides does a quadrilateral have?
6
3
5
4
A quadrilateral is defined as a polygon with exactly four sides. This is one of its most basic properties.
Which quadrilateral has four equal sides and four right angles?
Trapezoid
Rectangle
Square
Rhombus
A square is characterized by having both four equal sides and four right angles. This combination distinguishes it from rectangles and other quadrilaterals.
What is the sum of the interior angles of a triangle?
360°
180°
270°
90°
The sum of the interior angles of any triangle is always 180°. This fundamental rule is frequently used in geometry.
Which of the following is not a quadrilateral?
Rectangle
Pentagon
Square
Trapezoid
A pentagon has five sides, which means it does not meet the definition of a quadrilateral. Quadrilaterals must have exactly four sides.
What is the formula for finding the sum of interior angles in an n-sided polygon?
n - 2
180 + n
n x 180
180(n-2)
The sum of the interior angles of an n-sided polygon is given by 180(n-2). This formula is derived from dividing the polygon into (n-2) triangles.
Which quadrilateral has only one pair of parallel sides?
Square
Rectangle
Trapezoid
Parallelogram
A trapezoid is defined by having exactly one pair of parallel sides. The other options all have two pairs of parallel sides or do not satisfy the condition.
What distinguishes a concave polygon from a convex polygon?
Every vertex points outward
At least one interior angle greater than 180°
All interior angles less than 180°
It has curved sides
A concave polygon has at least one interior angle greater than 180°, causing one of its vertices to point inward. In contrast, convex polygons have all interior angles less than 180°.
Which quadrilateral has opposite sides that are both parallel and equal in length?
Kite
Trapezoid
Irregular Quadrilateral
Parallelogram
A parallelogram is defined by having both pairs of opposite sides parallel and equal in length. This is a key property differentiating it from other quadrilaterals.
What is the measure of each interior angle of a regular hexagon?
90°
120°
100°
140°
A regular hexagon has a total interior angle sum of 720°, and since all angles are equal, each angle measures 720°/6 = 120°. This property is typical for regular polygons.
Which statement best describes a square?
A quadrilateral with unequal sides
A quadrilateral with diagonals that are always unequal
A quadrilateral with only one pair of parallel sides
A quadrilateral with four equal sides and four right angles
A square is defined by both having four equal sides and four right angles. This distinguishes it from rectangles, which may not have equal sides, and other quadrilaterals.
How many diagonals does a pentagon have?
5
3
10
7
The number of diagonals in an n-sided polygon is given by the formula n(n-3)/2. For a pentagon, this calculation yields 5 diagonals.
Which quadrilateral always has perpendicular diagonals?
Parallelogram
Rhombus
Rectangle
Trapezoid
A defining property of a rhombus is that its diagonals are perpendicular bisectors of each other. This is not generally true for the other quadrilaterals listed.
Which of the following is always true for convex polygons?
They can have curved sides
At least one interior angle is greater than 180°
Every interior angle is less than 180°
They always have equal side lengths
A convex polygon is characterized by having all interior angles less than 180°. This ensures that any line segment drawn between two points inside the polygon remains within the shape.
In a parallelogram, what is true about its diagonals?
They do not intersect
They are always equal in length
They bisect each other
They are perpendicular
A fundamental property of parallelograms is that their diagonals bisect each other. This means that the point where the diagonals intersect divides each diagonal into two equal segments.
A quadrilateral has vertices at (0,0), (4,0), (3,3), and (0,4). Which type of quadrilateral is it?
Kite
Trapezoid
Rectangle
Square
Calculating the distances between the vertices shows that there are two distinct pairs of adjacent sides with equal lengths and the diagonals intersect perpendicularly. These characteristics define a kite.
What is the sum of the exterior angles of any convex polygon?
n x 180°
It depends on the number of sides
180°
360°
Regardless of the number of sides, the sum of the exterior angles of any convex polygon is always 360°. This is a well-known property in geometry.
If one interior angle of a regular octagon is increased by 10°, what happens to the sum of the interior angles?
It becomes 1090°
It increases by 10°
It remains 1080°
It decreases by 10°
The sum of the interior angles of an octagon is determined solely by the number of sides (using the formula 180(n-2)). Altering a single angle does not change the overall sum, which remains 1080°.
Which property distinguishes a rhombus from a generic parallelogram?
Opposite sides are parallel
All angles are right angles
All sides have equal length
Diagonals bisect each other
While both a parallelogram and a rhombus have opposite sides parallel and diagonals that bisect each other, a rhombus is uniquely defined by having all four sides of equal length.
In a cyclic quadrilateral, what is the relationship between opposite angles?
Opposite angles are equal
The sum of opposite angles is 180°
All angles are congruent
Adjacent angles sum to 180°
A cyclic quadrilateral is one whose vertices all lie on a circle, and a key property is that the sum of each pair of opposite angles equals 180°. This relationship is a classic result in circle geometry.
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Study Outcomes

  1. Identify key properties and definitions of polygons and quadrilaterals.
  2. Analyze and classify various types of quadrilaterals by their characteristics.
  3. Determine relationships between interior and exterior angles in polygons.
  4. Solve problems using the properties of polygons and quadrilaterals.
  5. Evaluate common misconceptions to strengthen understanding of geometric rules.

Unit 6 Answer Key: Polygons & Quadrilaterals Cheat Sheet

  1. What is a Quadrilateral? - A quadrilateral is a four-sided polygon with four vertices and interior angles that always add up to 360°. Imagine a shape party where the sum of all angles is the guest of honor! GeeksforGeeks: Quadrilateral Basics
  2. Common Quadrilateral Types - Squares, rectangles, rhombuses, parallelograms, trapezoids, and kites each flaunt unique side lengths, angles, and symmetries. Get to know their signature traits so you can spot them in any geometry lineup. GeeksforGeeks: Quadrilateral Overview
  3. Area Formulas Cheat Sheet - Every quadrilateral measures its space differently: square (side²), rectangle (length×width), parallelogram (base×height), rhombus & kite (½×d₝×d₂), trapezoid (½×(b₝+b₂)×height). Jot these down to ace your next quiz! GeeksforGeeks: Quadrilateral Formulas
  4. Perimeter Quick Guide - To find the boundary length, add all sides: 4×side for squares & rhombuses; 2×(length+width) for rectangles; sum every side for trapezoids; and use 2×(a+b) in kites and parallelograms. GeeksforGeeks: Perimeter Formulas
  5. Parallelogram Secrets - Opposite sides match in length and direction, opposite angles are twin buddies, and diagonals love to bisect each other. Think of it as the friendship bracelet of quadrilaterals! SparkNotes: Parallelogram Properties
  6. Rectangle Rules - A rectangle obeys parallelogram laws but adds four right angles, making it the go‑to shape for grids and screens. Bonus: its diagonals are equally assertive in length. e‑GMAT: Rectangle Properties
  7. Rhombus Rundown - All sides in a rhombus are lifelong pals of equal length, and its diagonals cross at perfect right angles. Picture two swords intersecting in a cool geometry duel! GeeksforGeeks: Rhombus Details
  8. Square Spotlight - The square is the ultimate mashup: a rectangle with equal sides and a rhombus with 90° angles. It's the all‑star athlete of quadrilaterals, versatile and powerful. GeeksforGeeks: Square Facts
  9. Trapezoid Tidbits - Only one pair of sides is parallel, but if the non‑parallel sides match, you get an isosceles trapezoid with equal base angles. It's geometry's runway model - balanced yet edgy! GeeksforGeeks: Trapezoid Insights
  10. Kite Insights - With two pairs of adjacent equal sides and one pair of opposite equal angles, a kite is geometry's toy in flight. Its diagonals intersect at right angles, keeping it steady up in the air. GeeksforGeeks: Kite Characteristics
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