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All questions of Special Types of Quadrilaterals for Class 8 Exam
In a parallelogram, how are the consecutive angles related?- a)They are equal
- b)They are complementary
- c)They are obtuse
- d)They are supplementary
Correct answer is option 'D'. Can you explain this answer?
In a parallelogram, how are the consecutive angles related?
a)
They are equal
b)
They are complementary
c)
They are obtuse
d)
They are supplementary
 | Trisha Vashisht answered |
In a parallelogram, consecutive angles are supplementary, meaning they add up to 180 degrees. This relationship arises from the parallel nature of opposite sides and is instrumental in solving various geometric problems involving parallelograms.
Which theorem states that the diagonals of a parallelogram bisect each other?- a)Theorem of Congruent Triangles
- b)Theorem of Parallel Lines
- c)Theorem of Opposite Angles
- d)Theorem of Diagonals
Correct answer is option 'D'. Can you explain this answer?
Which theorem states that the diagonals of a parallelogram bisect each other?
a)
Theorem of Congruent Triangles
b)
Theorem of Parallel Lines
c)
Theorem of Opposite Angles
d)
Theorem of Diagonals
 | EduRev Class 8 answered |
The theorem regarding the diagonals of a parallelogram asserts that they bisect each other, meaning that the point where the diagonals intersect divides each diagonal into two equal parts. This property is essential for proving other relationships in parallelograms and is widely used in geometric proofs.
Which of the following statements is true for all quadrilaterals?- a)The sum of the interior angles equals 360 degrees
- b)All sides are equal
- c)Opposite sides are parallel
- d)Diagonals are always equal
Correct answer is option 'A'. Can you explain this answer?
Which of the following statements is true for all quadrilaterals?
a)
The sum of the interior angles equals 360 degrees
b)
All sides are equal
c)
Opposite sides are parallel
d)
Diagonals are always equal
| | Trisha Vashisht answered |
The sum of the interior angles of any quadrilateral is always 360 degrees. This fundamental property is crucial for various geometric calculations and proofs, providing a basis for understanding more complex shapes.
In a rhombus, what is true about the angles?- a)Consecutive angles are supplementary
- b)All angles are acute
- c)All angles are obtuse
- d)All angles are right angles
Correct answer is option 'A'. Can you explain this answer?
In a rhombus, what is true about the angles?
a)
Consecutive angles are supplementary
b)
All angles are acute
c)
All angles are obtuse
d)
All angles are right angles
| | Trisha Vashisht answered |
In a rhombus, consecutive angles are supplementary, meaning they add up to 180 degrees. This property is essential for proving various relationships within the rhombus and helps in deriving other geometric conclusions.
Which of the following is a necessary condition for a quadrilateral to be classified as a rectangle?- a)Opposite sides must be unequal
- b)All sides must be equal
- c)Diagonals must be equal
- d)One angle must be 90 degrees
Correct answer is option 'C'. Can you explain this answer?
Which of the following is a necessary condition for a quadrilateral to be classified as a rectangle?
a)
Opposite sides must be unequal
b)
All sides must be equal
c)
Diagonals must be equal
d)
One angle must be 90 degrees
| | EduRev Class 8 answered |
To classify a quadrilateral as a rectangle, it is necessary that the diagonals are equal in length. This property, along with having opposite sides equal and parallel, helps in confirming the shape's classification as a rectangle.
In a rectangle, what can be said about the diagonals?- a)They are equal and bisect each other
- b)They are unequal and do not bisect
- c)They intersect at right angles
- d)They are equal but do not bisect
Correct answer is option 'A'. Can you explain this answer?
In a rectangle, what can be said about the diagonals?
a)
They are equal and bisect each other
b)
They are unequal and do not bisect
c)
They intersect at right angles
d)
They are equal but do not bisect
| | EduRev Class 8 answered |
In a rectangle, the diagonals are equal in length and bisect each other, which means they divide each other into two equal parts at the point of intersection. This property is significant in proving the congruence of triangles formed within the rectangle.
If a quadrilateral has equal opposite sides and opposite angles, what can be concluded about the shape?- a)It is a trapezium
- b)It is a rhombus
- c)It is a rectangle
- d)It is a parallelogram
Correct answer is option 'D'. Can you explain this answer?
If a quadrilateral has equal opposite sides and opposite angles, what can be concluded about the shape?
a)
It is a trapezium
b)
It is a rhombus
c)
It is a rectangle
d)
It is a parallelogram
| | EduRev Class 8 answered |
If a quadrilateral has both pairs of opposite sides equal and both pairs of opposite angles equal, it can be classified as a parallelogram. This property is fundamental in understanding various types of quadrilaterals and their relationships.
In a square, which of the following statements is true?- a)It has no parallel sides
- b)Diagonals are not equal
- c)All sides are equal and each angle is 90 degrees
- d)Only opposite sides are equal
Correct answer is option 'C'. Can you explain this answer?
In a square, which of the following statements is true?
a)
It has no parallel sides
b)
Diagonals are not equal
c)
All sides are equal and each angle is 90 degrees
d)
Only opposite sides are equal
| | Trisha Vashisht answered |
A square is characterized by having all sides equal in length and all angles measuring 90 degrees. This set of properties makes the square a special case of both a rectangle and a rhombus, combining the unique features of both shapes into one.
What is a key characteristic of a parallelogram?- a)Each angle measures 90 degrees
- b)Only one pair of sides is equal
- c)Opposite sides are both equal and parallel
- d)All sides are equal
Correct answer is option 'C'. Can you explain this answer?
What is a key characteristic of a parallelogram?
a)
Each angle measures 90 degrees
b)
Only one pair of sides is equal
c)
Opposite sides are both equal and parallel
d)
All sides are equal
| | Trisha Vashisht answered |
A parallelogram is defined by having both pairs of opposite sides that are equal in length and parallel. This property is fundamental in establishing other characteristics of parallelograms, such as the equality of opposite angles and the congruence of triangles formed by its diagonals.
Which quadrilateral has equal diagonals and opposite sides that are parallel?- a)Rhombus
- b)Parallelogram
- c)Trapezium
- d)Rectangle
Correct answer is option 'D'. Can you explain this answer?
Which quadrilateral has equal diagonals and opposite sides that are parallel?
a)
Rhombus
b)
Parallelogram
c)
Trapezium
d)
Rectangle
| | EduRev Class 8 answered |
A rectangle has equal diagonals and opposite sides that are parallel. This property, along with right angles, distinguishes it from other quadrilaterals, making it a specific type of parallelogram with additional characteristics.
To prove that a quadrilateral is a rectangle, which of the following is NOT a valid method?- a)Show all angles are 90 degrees
- b)Show all sides are equal
- c)Show it is a parallelogram with one angle equal to 90 degrees
- d)Show it is a parallelogram with equal diagonals
Correct answer is option 'A'. Can you explain this answer?
To prove that a quadrilateral is a rectangle, which of the following is NOT a valid method?
a)
Show all angles are 90 degrees
b)
Show all sides are equal
c)
Show it is a parallelogram with one angle equal to 90 degrees
d)
Show it is a parallelogram with equal diagonals
| | Trisha Vashisht answered |
A rectangle is characterized by having all angles equal to 90 degrees, and while it can be shown to be a parallelogram with specific properties, proving all sides are equal would classify the shape as a square, not a rectangle. This distinction is crucial in understanding the hierarchy of quadrilateral properties.
Which condition is NOT necessary to prove that a quadrilateral is a parallelogram?- a)Opposite angles are equal
- b)Opposite sides are equal
- c)Diagonals bisect each other
- d)All angles are equal
Correct answer is option 'B'. Can you explain this answer?
Which condition is NOT necessary to prove that a quadrilateral is a parallelogram?
a)
Opposite angles are equal
b)
Opposite sides are equal
c)
Diagonals bisect each other
d)
All angles are equal
| | EduRev Class 8 answered |
While proving a quadrilateral is a parallelogram, it is not necessary for all angles to be equal. Instead, it's sufficient to show that either opposite sides are equal, opposite angles are equal, or that diagonals bisect each other. This flexibility allows for various approaches to establish the classification of the quadrilateral.
If diagonals of a quadrilateral bisect each other, which of the following could be true?- a)It is always a rhombus
- b)It cannot be a trapezium
- c)It is always a rectangle
- d)It is a parallelogram
Correct answer is option 'D'. Can you explain this answer?
If diagonals of a quadrilateral bisect each other, which of the following could be true?
a)
It is always a rhombus
b)
It cannot be a trapezium
c)
It is always a rectangle
d)
It is a parallelogram
| | Trisha Vashisht answered |
If the diagonals of a quadrilateral bisect each other, the quadrilateral must be a parallelogram. While rectangles and rhombuses also have this property, it does not exclusively define them, as other shapes can exhibit this behavior as well.
Which of the following quadrilaterals has one pair of opposite sides that are parallel?- a)Trapezium
- b)Rhombus
- c)Square
- d)Rectangle
Correct answer is option 'A'. Can you explain this answer?
Which of the following quadrilaterals has one pair of opposite sides that are parallel?
a)
Trapezium
b)
Rhombus
c)
Square
d)
Rectangle
| | EduRev Class 8 answered |
A trapezium is defined as a quadrilateral with at least one pair of opposite sides that are parallel. This distinguishes it from other quadrilaterals like rectangles and squares, which have both pairs of opposite sides parallel. Understanding this property is crucial in geometry as it helps classify quadrilaterals based on their side relationships.
What property do the diagonals of a square possess?- a)They are parallel
- b)They bisect each other at 90 degrees
- c)They are unequal
- d)They do not bisect
Correct answer is option 'B'. Can you explain this answer?
What property do the diagonals of a square possess?
a)
They are parallel
b)
They bisect each other at 90 degrees
c)
They are unequal
d)
They do not bisect
| | Trisha Vashisht answered |
The diagonals of a square bisect each other at right angles (90 degrees) and are also equal in length. This unique combination of properties makes the square a versatile shape in geometry, allowing for various proofs and applications.
What is the defining property of an isosceles trapezium?- a)All sides are equal
- b)One pair of opposite sides is equal
- c)The non-parallel sides are equal
- d)All angles are equal
Correct answer is option 'C'. Can you explain this answer?
What is the defining property of an isosceles trapezium?
a)
All sides are equal
b)
One pair of opposite sides is equal
c)
The non-parallel sides are equal
d)
All angles are equal
| | Trisha Vashisht answered |
An isosceles trapezium is defined by having one pair of parallel sides, called bases, and the non-parallel sides, or legs, being equal in length. This property leads to additional angle and diagonal relationships that are useful in geometric analysis.
How can you prove that a quadrilateral is a rhombus?- a)Show that the diagonals are unequal
- b)Show that all angles are right angles
- c)Show that all sides are equal
- d)Show that opposite sides are unequal
Correct answer is option 'C'. Can you explain this answer?
How can you prove that a quadrilateral is a rhombus?
a)
Show that the diagonals are unequal
b)
Show that all angles are right angles
c)
Show that all sides are equal
d)
Show that opposite sides are unequal
| | Trisha Vashisht answered |
To prove that a quadrilateral is a rhombus, one can demonstrate that all sides are equal in length. This property is unique to rhombuses and is critical in establishing their geometric identity, differentiating them from other quadrilaterals.
Which of the following properties is unique to a rhombus?- a)All angles are 90 degrees
- b)All sides are equal
- c)Only opposite sides are parallel
- d)Diagonals are equal
Correct answer is option 'B'. Can you explain this answer?
Which of the following properties is unique to a rhombus?
a)
All angles are 90 degrees
b)
All sides are equal
c)
Only opposite sides are parallel
d)
Diagonals are equal
| | EduRev Class 8 answered |
A rhombus is defined by having all four sides equal in length. While it shares some properties with rectangles and squares, such as having parallel opposite sides, the equality of all sides is a unique characteristic that distinguishes it from other quadrilaterals.
What can be concluded if a quadrilateral has at least one pair of parallel sides?- a)It is a rectangle
- b)It is a trapezium
- c)It is a parallelogram
- d)It is a square
Correct answer is option 'B'. Can you explain this answer?
What can be concluded if a quadrilateral has at least one pair of parallel sides?
a)
It is a rectangle
b)
It is a trapezium
c)
It is a parallelogram
d)
It is a square
| | Trisha Vashisht answered |
If a quadrilateral has at least one pair of parallel sides, it can be classified as a trapezium. This classification is essential in distinguishing trapeziums from other types of quadrilaterals, such as parallelograms, rectangles, and squares, which have more specific properties.
In an isosceles trapezium, which of the following statements is true regarding the angles?- a)The diagonals are not equal
- b)Opposite angles next to the bases are equal
- c)All angles are equal
- d)Consecutive angles are supplementary
Correct answer is option 'B'. Can you explain this answer?
In an isosceles trapezium, which of the following statements is true regarding the angles?
a)
The diagonals are not equal
b)
Opposite angles next to the bases are equal
c)
All angles are equal
d)
Consecutive angles are supplementary
| | EduRev Class 8 answered |
In an isosceles trapezium, the angles adjacent to each base are equal, meaning that if one angle is known, the other can be determined. This property helps in solving various geometric problems involving trapeziums and also aids in proving other properties related to isosceles trapeziums.
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