What Do You Know About Trapezoid?
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.
- 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 trianglesExplanation
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.Rate this question:
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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. 0Explanation
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.Rate this question:
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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 degreesExplanation
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.Rate this question:
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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 partsExplanation
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.Rate this question:
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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 anglesExplanation
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.Rate this question:
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- 6.
A trapezoid as a quadrilateral is _________?
- A.
Concave
- B.
Convex
- C.
Supplementary
- D.
Complementary
Correct Answer
A. ConcaveExplanation
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.Rate this question:
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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 trapezoidExplanation
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.Rate this question:
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- 8.
A parallelogram is a trapezoid with _____ parallel sides?
- A.
Two
- B.
Eight
- C.
Four
- D.
Six
Correct Answer
A. TwoExplanation
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.Rate this question:
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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. CircumferenceExplanation
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.Rate this question:
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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 lawExplanation
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.Rate this question:
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Mar 20, 2023Quiz Edited by
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Jun 12, 2018Quiz Created by
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