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Which of the following statements is correct with respect to a parallelogram?
1. Diagonals bisect each other.
2. Adjacent angles are supplementary.
3. Opposite sides are equal.
4. Opposite sides are parallel
1. Diagonals bisect each other.
2. Adjacent angles are supplementary.
3. Opposite sides are equal.
4. Opposite sides are parallel
- a)Statement 1 only
- b)Statements 1,2,3 and 4
- c)Statements 1 and 4
- d)Statements 3 and 4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Which of the following statements is correct with respect to a paralle...
These all are the properties that are present in a parallelogram that's why option b is correct.
¹. The diagonals of parallelogram bisect each other means they equally divide each other.
². Adjacent sides of parallelogram are supplementary means the sum of the adjacent sides of parallelogram is 180 degree.
³. The opposite sides are equal in length of parallelogram and parallel also .
¹. The diagonals of parallelogram bisect each other means they equally divide each other.
². Adjacent sides of parallelogram are supplementary means the sum of the adjacent sides of parallelogram is 180 degree.
³. The opposite sides are equal in length of parallelogram and parallel also .
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Which of the following statements is correct with respect to a paralle...
Statement 1: Diagonals bisect each other
- The diagonals of a parallelogram are the line segments connecting the opposite vertices.
- In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts.
- This property can be proved using congruent triangles and the properties of parallel lines.
Statement 2: Adjacent angles are supplementary
- Adjacent angles are angles that share a common side and a common vertex.
- In a parallelogram, opposite angles are congruent, which means they have the same measure.
- Since the sum of the measures of two adjacent angles forms a straight angle (180 degrees), adjacent angles in a parallelogram are supplementary.
Statement 3: Opposite sides are equal
- In a parallelogram, opposite sides are parallel, meaning they never intersect.
- By definition, parallel lines have the same slope.
- Therefore, the lengths of the opposite sides of a parallelogram are equal.
Statement 4: Opposite sides are parallel
- As mentioned earlier, opposite sides of a parallelogram are parallel.
- This is a defining property of a parallelogram.
Combining the Statements
- Looking at the properties mentioned in all the statements, it is clear that they are all true for a parallelogram.
- The diagonals bisect each other, adjacent angles are supplementary, opposite sides are equal, and opposite sides are parallel.
- Therefore, the correct answer is option 'B', which includes all the given statements.
Summary
- In a parallelogram, the diagonals bisect each other, adjacent angles are supplementary, opposite sides are equal, and opposite sides are parallel.
- These properties can be proven using geometric principles and the definition of a parallelogram.
- The correct answer is option 'B', which includes all the given statements.
- The diagonals of a parallelogram are the line segments connecting the opposite vertices.
- In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts.
- This property can be proved using congruent triangles and the properties of parallel lines.
Statement 2: Adjacent angles are supplementary
- Adjacent angles are angles that share a common side and a common vertex.
- In a parallelogram, opposite angles are congruent, which means they have the same measure.
- Since the sum of the measures of two adjacent angles forms a straight angle (180 degrees), adjacent angles in a parallelogram are supplementary.
Statement 3: Opposite sides are equal
- In a parallelogram, opposite sides are parallel, meaning they never intersect.
- By definition, parallel lines have the same slope.
- Therefore, the lengths of the opposite sides of a parallelogram are equal.
Statement 4: Opposite sides are parallel
- As mentioned earlier, opposite sides of a parallelogram are parallel.
- This is a defining property of a parallelogram.
Combining the Statements
- Looking at the properties mentioned in all the statements, it is clear that they are all true for a parallelogram.
- The diagonals bisect each other, adjacent angles are supplementary, opposite sides are equal, and opposite sides are parallel.
- Therefore, the correct answer is option 'B', which includes all the given statements.
Summary
- In a parallelogram, the diagonals bisect each other, adjacent angles are supplementary, opposite sides are equal, and opposite sides are parallel.
- These properties can be proven using geometric principles and the definition of a parallelogram.
- The correct answer is option 'B', which includes all the given statements.
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