Class 9 Exam > Class 9 Questions > If a diagonal AC and BD of a quadrilateral AB...
Start Learning for Free
If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is a
- a)Rectangle
- b)Triangle
- c)Rhombus
- d)Parallelogram
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If a diagonal AC and BD of a quadrilateral ABCD bisect each other, the...
Free Test
FREE
| Start Free Test |
Community Answer
If a diagonal AC and BD of a quadrilateral ABCD bisect each other, the...
Explanation:
To prove that quadrilateral ABCD is a parallelogram, we need to show that opposite sides are parallel.
Given:
- Diagonal AC and BD of quadrilateral ABCD bisect each other.
Proof:
We can prove that ABCD is a parallelogram by using the properties of diagonals in a quadrilateral.
1. Diagonals of a parallelogram bisect each other:
In a parallelogram, the diagonals bisect each other. Since the given quadrilateral has diagonals that bisect each other, it suggests that ABCD could be a parallelogram.
2. Diagonals of a parallelogram divide it into congruent triangles:
In a parallelogram, the diagonals divide it into four congruent triangles. If the given quadrilateral has diagonals that bisect each other, it implies that the resulting triangles formed by the diagonals are congruent.
3. Congruent triangles have equal corresponding angles and sides:
If the four triangles formed by the diagonals are congruent, it means they have equal corresponding angles and sides.
4. Opposite angles of a parallelogram are congruent:
In a parallelogram, opposite angles are congruent. Since the congruent triangles formed by the diagonals have equal corresponding angles, it suggests that opposite angles of ABCD are congruent.
5. Opposite sides of a parallelogram are parallel:
If opposite angles of ABCD are congruent, it implies that opposite sides are parallel. Hence, ABCD is a parallelogram.
Therefore, based on the properties of diagonals in a quadrilateral, we can conclude that if diagonal AC and BD of quadrilateral ABCD bisect each other, then ABCD is a parallelogram (option D).
To prove that quadrilateral ABCD is a parallelogram, we need to show that opposite sides are parallel.
Given:
- Diagonal AC and BD of quadrilateral ABCD bisect each other.
Proof:
We can prove that ABCD is a parallelogram by using the properties of diagonals in a quadrilateral.
1. Diagonals of a parallelogram bisect each other:
In a parallelogram, the diagonals bisect each other. Since the given quadrilateral has diagonals that bisect each other, it suggests that ABCD could be a parallelogram.
2. Diagonals of a parallelogram divide it into congruent triangles:
In a parallelogram, the diagonals divide it into four congruent triangles. If the given quadrilateral has diagonals that bisect each other, it implies that the resulting triangles formed by the diagonals are congruent.
3. Congruent triangles have equal corresponding angles and sides:
If the four triangles formed by the diagonals are congruent, it means they have equal corresponding angles and sides.
4. Opposite angles of a parallelogram are congruent:
In a parallelogram, opposite angles are congruent. Since the congruent triangles formed by the diagonals have equal corresponding angles, it suggests that opposite angles of ABCD are congruent.
5. Opposite sides of a parallelogram are parallel:
If opposite angles of ABCD are congruent, it implies that opposite sides are parallel. Hence, ABCD is a parallelogram.
Therefore, based on the properties of diagonals in a quadrilateral, we can conclude that if diagonal AC and BD of quadrilateral ABCD bisect each other, then ABCD is a parallelogram (option D).
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Top Courses for Class 9View all
If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer?
Question Description
If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. 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 If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. 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 If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer?.
If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. 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 If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. 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 If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer?.
Solutions for If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If a diagonal AC and BD of a quadrilateral ABCD bisect each other, then ABCD is aa)Rectangleb)Trianglec)Rhombusd)ParallelogramCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup