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Statement 1: AB||DC and AD||BC
Statement 2: AB = DC and AD=BC or a quadrilateral ABCD to be a parallelogram,__________
- a)Both Statement 1 and Statement 2 should be true.
- b)Either Statement 1 or Statement 2 should be true
- c)Only Statement 1 should be true.
- d)Only Statement 2 should be true
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Statement 1: AB||DC and AD||BCStatement 2: AB = DC and AD=BC or a quad...
ABCD is quadrilateral. AB=CD and AD=BC
Since the opposite sides of the quadrilateral are equal and AB parallel to DC. Therefore, the quadrilateral ABCD is a parallelogram.
hence, opposite sides are parallel to each other.
Or, AB∥CD and AD∥BC
Since the opposite sides of the quadrilateral are equal and AB parallel to DC. Therefore, the quadrilateral ABCD is a parallelogram.
hence, opposite sides are parallel to each other.
Or, AB∥CD and AD∥BC
Most Upvoted Answer
Statement 1: AB||DC and AD||BCStatement 2: AB = DC and AD=BC or a quad...
To determine whether a quadrilateral ABCD is a parallelogram, we need to analyze the given statements.
Statement 1: AB||DC and AD||BC
This statement states that AB is parallel to DC and AD is parallel to BC. In a parallelogram, opposite sides are parallel, so this statement aligns with the definition of a parallelogram.
Statement 2: AB = DC and AD = BC
This statement states that AB is equal to DC and AD is equal to BC. In a parallelogram, opposite sides are equal in length, so this statement also aligns with the definition of a parallelogram.
Explanation:
The given statements are both necessary conditions for a quadrilateral to be a parallelogram. In other words, both parallel sides and equal lengths of opposite sides are required for a quadrilateral to be a parallelogram.
If either statement 1 or statement 2 is true, it satisfies one of the necessary conditions for a parallelogram. If statement 1 is true, it satisfies the condition of parallel sides. If statement 2 is true, it satisfies the condition of equal lengths of opposite sides.
Therefore, if either statement 1 or statement 2 is true, the quadrilateral ABCD can be classified as a parallelogram. Hence, the correct answer is option 'A' - Either Statement 1 or Statement 2 should be true.
Statement 1: AB||DC and AD||BC
This statement states that AB is parallel to DC and AD is parallel to BC. In a parallelogram, opposite sides are parallel, so this statement aligns with the definition of a parallelogram.
Statement 2: AB = DC and AD = BC
This statement states that AB is equal to DC and AD is equal to BC. In a parallelogram, opposite sides are equal in length, so this statement also aligns with the definition of a parallelogram.
Explanation:
The given statements are both necessary conditions for a quadrilateral to be a parallelogram. In other words, both parallel sides and equal lengths of opposite sides are required for a quadrilateral to be a parallelogram.
If either statement 1 or statement 2 is true, it satisfies one of the necessary conditions for a parallelogram. If statement 1 is true, it satisfies the condition of parallel sides. If statement 2 is true, it satisfies the condition of equal lengths of opposite sides.
Therefore, if either statement 1 or statement 2 is true, the quadrilateral ABCD can be classified as a parallelogram. Hence, the correct answer is option 'A' - Either Statement 1 or Statement 2 should be true.
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Statement 1: AB||DC and AD||BCStatement 2: AB = DC and AD=BC or a quadrilateral ABCD to be a parallelogram,__________a)Both Statement 1 and Statement 2 should be true.b)Either Statement 1 or Statement 2 should be truec)Only Statement 1 should be true.d)Only Statement 2 should be trueCorrect answer is option 'A'. Can you explain this answer?
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Statement 1: AB||DC and AD||BCStatement 2: AB = DC and AD=BC or a quadrilateral ABCD to be a parallelogram,__________a)Both Statement 1 and Statement 2 should be true.b)Either Statement 1 or Statement 2 should be truec)Only Statement 1 should be true.d)Only Statement 2 should be trueCorrect answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Statement 1: AB||DC and AD||BCStatement 2: AB = DC and AD=BC or a quadrilateral ABCD to be a parallelogram,__________a)Both Statement 1 and Statement 2 should be true.b)Either Statement 1 or Statement 2 should be truec)Only Statement 1 should be true.d)Only Statement 2 should be trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement 1: AB||DC and AD||BCStatement 2: AB = DC and AD=BC or a quadrilateral ABCD to be a parallelogram,__________a)Both Statement 1 and Statement 2 should be true.b)Either Statement 1 or Statement 2 should be truec)Only Statement 1 should be true.d)Only Statement 2 should be trueCorrect answer is option 'A'. Can you explain this answer?.
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