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Quizzes > Mathematics > Geometry

Quadrilateral Quiz: Can You Name Every Four-Sided Shape?

Think you know what makes a kite or rhombus a quadrilateral? Dive in!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art kites rhombuses and other quadrilaterals on a golden yellow background for a free quadrilateral quiz.

Ready to sharpen your geometry chops? Our Ultimate Quadrilateral Quiz is here to challenge and educate both students and enthusiasts alike. Whether you've wondered if a kite is ____ a quadrilateral or pondered that a rhombus is ____ a quadrilateral, this free quadrilateral quiz will guide you through every shape's secrets. Take the quadrilateral test to classify kites, rectangles, trapezoids and beyond as you track your progress. Curious minds can dive into the free quadrilateral challenge , then test on quadrilaterals to boost your confidence. Embrace the fun, learn faster, and ace your next geometry class now!

What is the sum of the interior angles of any quadrilateral?
540°
360°
180°
720°
The sum of interior angles in an n-sided polygon is (n - 2)×180°. For a quadrilateral, n=4 gives (4 - 2)×180°=360°. This holds true for all simple quadrilaterals. Source
Which quadrilateral has four equal sides and four right angles?
Square
Rhombus
Parallelogram
Rectangle
A square has all four sides equal and every angle is 90°. A rhombus has equal sides but not necessarily right angles. A rectangle has right angles but not all equal sides. Source
In which quadrilateral are opposite sides parallel and all angles are right angles?
Rectangle
Parallelogram
Square
Kite
A rectangle is defined by having opposite sides parallel and all four interior angles equal to 90°. A square meets these criteria but is a special case of a rectangle. Parallelograms have equal opposite angles but not necessarily right angles. Source
A quadrilateral with exactly one pair of parallel sides is called what?
Kite
Rhombus
Trapezoid
Parallelogram
A trapezoid is defined as a four-sided figure with only one pair of parallel sides. Kites have two pairs of adjacent equal sides. Parallelograms have two pairs of parallel sides. Source
In a rhombus, the diagonals always:
Are perpendicular and bisect each other
Are equal in length
Are parallel
Never meet
Rhombus diagonals intersect at 90° and each diagonal cuts the other into two equal segments. They also bisect the interior angles of the rhombus. They are not generally equal in length. Source
What is the sum of the exterior angles of any convex quadrilateral, one at each vertex?
720°
540°
180°
360°
The sum of one exterior angle at each vertex of any convex polygon is always 360°, regardless of the number of sides. This follows from the fact that exterior and interior angles at each vertex sum to 180°. Source
Which quadrilateral always has congruent diagonals?
Trapezoid
Rhombus
Kite
Rectangle
Rectangles have diagonals of equal length because they are congruent right triangles joined. Rhombus and kite diagonals are generally not equal. Trapezoid diagonals are not guaranteed to be congruent. Source
A kite has how many pairs of adjacent equal sides?
2
4
1
3
A kite is defined by having two distinct pairs of adjacent sides that are equal in length. The other two sides are generally non-equal. Source
Given vertices A(0,0), B(4,0), C(3,3), D(-1,3) in the plane, what type of quadrilateral is ABCD?
Trapezoid
Square
Rectangle
Parallelogram
Opposite sides AB and CD are parallel and equal in length, and BC and DA are also parallel and equal. There are no right angles, so it is a general parallelogram. Source
What is the area of a trapezoid with bases of lengths 10 and 6 and a height of 5?
80
16
32
40
The area formula for a trapezoid is ((base? + base?) / 2) × height. Substituting gives ((10 + 6)/2)×5 = 8×5 = 40. Source
In a cyclic quadrilateral (one inscribed in a circle), the sum of a pair of opposite angles is always:
270°
180°
360°
90°
Opposite angles of a cyclic quadrilateral sum to 180° due to the inscribed angle theorem. This is a defining property of cyclic quadrilaterals. Source
Bretschneider's formula gives the area of any quadrilateral as ?((s - a)(s - b)(s - c)(s - d) - abcd·cos²((A+C)/2)). For which special case does this reduce to ?((s - a)(s - b)(s - c)(s - d))?
Parallelogram
Cyclic quadrilateral
Kite
Rectangle
When a quadrilateral is cyclic, opposite angles A and C sum to 180°, so (A+C)/2=90° and cos²90°=0. This eliminates the cosine term, giving Brahmagupta's formula. Source
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Study Outcomes

  1. Identify Quadrilateral Types -

    List and describe major four-sided shapes - kite, rhombus, square, parallelogram - by their defining attributes.

  2. Classify Quadrilateral Relationships -

    Distinguish statements such as "a kite is ____ a quadrilateral" and "a rhombus is ____ a quadrilateral" using precise geometric reasoning.

  3. Apply Definitions in the Quadrilateral Quiz -

    Use formal definitions to accurately complete questions in the quadrilateral quiz and reinforce understanding of each shape.

  4. Analyze Side and Angle Properties -

    Examine and explain how side lengths and angle measures determine specific quadrilateral categories.

  5. Evaluate Responses in the Quadrilateral Test -

    Assess answer choices in the quadrilateral test and test on quadrilaterals to ensure correctness and depth of understanding.

  6. Enhance Geometry Problem-Solving Skills -

    Develop strategies to approach future geometry challenges confidently by reflecting on quiz performance.

Cheat Sheet

  1. Hierarchy of Quadrilateral Types -

    Understanding the hierarchy of quadrilateral types helps in any quadrilateral quiz or quadrilateral test. Visualize a Venn diagram with general quadrilaterals, parallelograms, trapezoids, kites and special cases like rectangles, rhombuses and squares for quick identification (source: Khan Academy).

  2. Identifying a Kite -

    In geometry, a kite is a quadrilateral with two distinct pairs of adjacent congruent sides and perpendicular diagonals (source: MathisFun). Remember "kite diagonals cross at right angles" as a quick mnemonic for your next "a kite is ____ a quadrilateral" question.

  3. Understanding a Rhombus -

    A rhombus is a quadrilateral with all four sides equal and opposite sides parallel; hence, a rhombus is also a parallelogram (source: University of Cambridge). Its diagonals bisect opposite angles at 90°, a handy fact for "a rhombus is ____ a quadrilateral" prompts.

  4. Interior Angle Sum Formula -

    Every quadrilateral has an interior angle sum of (4−2)×180° = 360°, a fundamental formula for any quadrilateral quiz (source: MIT OpenCourseWare). For example, if three angles are 80°, 110° and 95°, the fourth angle is 360°−(80°+110°+95°)=75°.

  5. Area Formulas for Key Quadrilaterals -

    Memorize key area formulas for your quadrilateral test: rectangle A = l·w, parallelogram A = b·h, trapezoid A = (b1 + b2)/2·h and kite A = (d1·d2)/2 (source: British Mathematical Olympiad). For instance, a kite with diagonals 8 cm and 6 cm has area (8×6)/2 = 24 cm².

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