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DIRECTIONS for the question:
Solve the following question and mark the best possible option.
Solve the following question and mark the best possible option.
Which of the following statements is definitely true?
- a)All the angles of parallelogram can be acute
- b)If the diagonals of a quadrilateral are at right angles, it is a rhombus
- c)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangle
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
DIRECTIONS for the question: Solve the following question and mark the...
If all the angles in a parallelogram are acute, their sum cannot be 360°. So option 1 is false.
Option 2 is not necessarily true as the diagonals of a kite are also perpendicular to each other. Consider option 3.
Each diagonal of a quadrilateral divides it into 2 triangles. So, the lines joining the mid-points of the sides will be parallel to the diagonals and their lengths will be half the lengths of the corresponding diagonals. So, the figure formed will be a parallelogram.
Since the diagonals are perpendicular to each other, the sides of the parallelogram formed will be perpendicular to each other.
In other words, the parallelogram formed is a rectangle.
Thus option 3 is true.
Most Upvoted Answer
DIRECTIONS for the question: Solve the following question and mark the...
Explanation:
To determine which statement is definitely true, let's analyze each option one by one.
a) All the angles of parallelogram can be acute:
This statement is not definitely true. A parallelogram can have acute angles, obtuse angles, or both. So, this option is incorrect.
b) If the diagonals of a quadrilateral are at right angles, it is a rhombus:
This statement is also not definitely true. While it is true that a rhombus has diagonals that are at right angles to each other, there are other quadrilaterals, such as a square, that also have diagonals at right angles. So, this option is incorrect.
c) If the diagonals of a quadrilateral are at right angles, the figure formed by joining the midpoints of adjacent sides is a rectangle:
This statement is definitely true. When the diagonals of a quadrilateral are at right angles, the figure formed by joining the midpoints of adjacent sides is always a rectangle. This is a known property of quadrilaterals. So, this option is correct.
d) None of these:
Since option c is definitely true, option d is incorrect.
Therefore, the correct answer is option c) If the diagonals of a quadrilateral are at right angles, the figure formed by joining the midpoints of adjacent sides is a rectangle.
To determine which statement is definitely true, let's analyze each option one by one.
a) All the angles of parallelogram can be acute:
This statement is not definitely true. A parallelogram can have acute angles, obtuse angles, or both. So, this option is incorrect.
b) If the diagonals of a quadrilateral are at right angles, it is a rhombus:
This statement is also not definitely true. While it is true that a rhombus has diagonals that are at right angles to each other, there are other quadrilaterals, such as a square, that also have diagonals at right angles. So, this option is incorrect.
c) If the diagonals of a quadrilateral are at right angles, the figure formed by joining the midpoints of adjacent sides is a rectangle:
This statement is definitely true. When the diagonals of a quadrilateral are at right angles, the figure formed by joining the midpoints of adjacent sides is always a rectangle. This is a known property of quadrilaterals. So, this option is correct.
d) None of these:
Since option c is definitely true, option d is incorrect.
Therefore, the correct answer is option c) If the diagonals of a quadrilateral are at right angles, the figure formed by joining the midpoints of adjacent sides is a rectangle.
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DIRECTIONS for the question: Solve the following question and mark the best possible option.Which of the following statements is definitely true?a)All the angles of parallelogram can be acuteb)If the diagonals of a quadrilateral are at right angles, it is a rhombusc)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangled)None of theseCorrect answer is option 'C'. Can you explain this answer?
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DIRECTIONS for the question: Solve the following question and mark the best possible option.Which of the following statements is definitely true?a)All the angles of parallelogram can be acuteb)If the diagonals of a quadrilateral are at right angles, it is a rhombusc)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangled)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for the question: Solve the following question and mark the best possible option.Which of the following statements is definitely true?a)All the angles of parallelogram can be acuteb)If the diagonals of a quadrilateral are at right angles, it is a rhombusc)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangled)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question: Solve the following question and mark the best possible option.Which of the following statements is definitely true?a)All the angles of parallelogram can be acuteb)If the diagonals of a quadrilateral are at right angles, it is a rhombusc)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangled)None of theseCorrect answer is option 'C'. Can you explain this answer?.
DIRECTIONS for the question: Solve the following question and mark the best possible option.Which of the following statements is definitely true?a)All the angles of parallelogram can be acuteb)If the diagonals of a quadrilateral are at right angles, it is a rhombusc)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangled)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for the question: Solve the following question and mark the best possible option.Which of the following statements is definitely true?a)All the angles of parallelogram can be acuteb)If the diagonals of a quadrilateral are at right angles, it is a rhombusc)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangled)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question: Solve the following question and mark the best possible option.Which of the following statements is definitely true?a)All the angles of parallelogram can be acuteb)If the diagonals of a quadrilateral are at right angles, it is a rhombusc)If the diagonals of a quadrilateral are at right angles, the figure formed by joining the mid points of adjacent sides is a rectangled)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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