What Do You Know About Trapezoid?

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What Do You Know About Trapezoid? - Quiz

A trapezoid is shape with four sides. In mathematics, the knowledge of trapezoid is governed by two schools of thought viz: inclusive and exclusive definition. The former presents the trapezoid as a four-sided shape with only a pair parallel sides. The later presents it as a four-sided shape with more than one pair of parallel sides. Show your mastery of Euclidean geometry by answering the following questions.


Questions and Answers
  • 1. 

    How many triangles does the diagonals of trapezoid form?

    • A.

      Four triangles

    • B.

      Two triangles

    • C.

      A triangle

    • D.

      Six triangles

    Correct Answer
    A. Four triangles
    Explanation
    The diagonals of a trapezoid form four triangles. The trapezoid has two bases and two legs. When the diagonals are drawn, they intersect at a point inside the trapezoid, creating four triangles. Each triangle is formed by connecting one of the endpoints of a base to the intersection point of the diagonals. Therefore, the correct answer is four triangles.

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  • 2. 

    What is the sum of the two cosines adjacent angle in a trapezoid?

    • A.

      1

    • B.

      2

    • C.

      90

    • D.

      0

    Correct Answer
    D. 0
    Explanation
    In a trapezoid, the sum of the two adjacent angles is always equal to 180 degrees. Since the cosine of 180 degrees is equal to -1, the sum of the two cosines adjacent angles in a trapezoid is 0.

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  • 3. 

    ................... degree implies that the quadrilateral is a trapezoid:  

    • A.

      180 degrees

    • B.

      170 degrees

    • C.

      165 degrees

    • D.

      45 degrees

    Correct Answer
    A. 180 degrees
    Explanation
    A trapezoid is a quadrilateral with at least one pair of parallel sides. The sum of the interior angles of any quadrilateral is always 360 degrees. However, in a trapezoid, one pair of opposite angles are supplementary, meaning they add up to 180 degrees. Therefore, if one angle in a quadrilateral is 180 degrees, it implies that the quadrilateral is a trapezoid.

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  • 4. 

    A bimedian divides a trapezoid to how many parts?

    • A.

      Two parts

    • B.

      Four parts

    • C.

      Six parts

    • D.

      Eight parts

    Correct Answer
    A. Two parts
    Explanation
    A bimedian divides a trapezoid into two parts. A bimedian is a line segment that connects the midpoints of the non-parallel sides of a trapezoid. It divides the trapezoid into two smaller trapezoids that are congruent to each other. Therefore, the correct answer is two parts.

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  • 5. 

    How many adjacent right angles does a right trapezoid has?

    • A.

      Four adjacent right angles

    • B.

      Six adjacent right angles

    • C.

      Eight adjacent right angles

    • D.

      Two adjacent right angles

    Correct Answer
    D. Two adjacent right angles
    Explanation
    A right trapezoid has two adjacent right angles. A right trapezoid is a quadrilateral with one pair of parallel sides and one pair of non-parallel sides. The non-parallel sides are typically referred to as the legs of the trapezoid, while the parallel sides are called the bases. Since a right trapezoid has one pair of parallel sides, it means that one pair of opposite angles are right angles. Therefore, there are two adjacent right angles in a right trapezoid.

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  • 6. 

    A trapezoid as a quadrilateral is _________?

    • A.

      Concave 

    • B.

      Convex 

    • C.

      Supplementary 

    • D.

      Complementary 

    Correct Answer
    A. Concave 
    Explanation
    A trapezoid is a convex quadrilateral, meaning that all of its interior angles are less than 180 degrees and all of its diagonals lie within the shape.

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  • 7. 

    The following are types of trapezoid except? 

    • A.

      Right trapezoid

    • B.

      Acute trapezoid

    • C.

      Complementary trapezoid

    • D.

      Left trapezoid

    Correct Answer
    C. Complementary trapezoid
    Explanation
    A trapezoid is a quadrilateral with at least one pair of parallel sides. A right trapezoid is a trapezoid where one of the angles is a right angle. An acute trapezoid is a trapezoid where all angles are acute angles. A left trapezoid is a trapezoid where the longer base is on the left side. However, there is no such thing as a complementary trapezoid. The term "complementary" refers to angles that add up to 90 degrees, which is not a characteristic of a trapezoid.

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  • 8. 

    A parallelogram is a trapezoid with _____ parallel sides?

    • A.

      Two

    • B.

      Eight

    • C.

      Four 

    • D.

      Six

    Correct Answer
    A. Two
    Explanation
    A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A trapezoid, on the other hand, is a quadrilateral with only one pair of opposite sides parallel. Therefore, a parallelogram can also be considered a trapezoid with two parallel sides.

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  • 9. 

    Which of the following terms does not correlate with a trapezoid?

    • A.

      Incircle

    • B.

      Right angle

    • C.

      Vertice

    • D.

      Circumference

    Correct Answer
    D. Circumference
    Explanation
    The term "circumference" does not correlate with a trapezoid. A trapezoid is a quadrilateral with one pair of parallel sides. The term "incircle" refers to a circle that is tangent to all four sides of a polygon, including a trapezoid. "Right angle" is a term that can be associated with a trapezoid if one of its angles measures 90 degrees. "Vertice" refers to the corners of a polygon, including a trapezoid. However, "circumference" is a term commonly used to describe the distance around a circle, which is not applicable to a trapezoid.

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  • 10. 

    The angles of a trapezoid obey which of these laws?

    • A.

      Pythagoras theorem

    • B.

      Sine law

    • C.

      Commutative law

    • D.

       Cosine law 

    Correct Answer
    B. Sine law
    Explanation
    The angles of a trapezoid obey the Sine law. The Sine law states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Since a trapezoid can be divided into two triangles, the Sine law can be applied to each triangle individually to determine the relationship between the angles. Therefore, the angles of a trapezoid follow the Sine law.

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  • Mar 20, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jun 12, 2018
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    Tunde1995
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