Class 9 Exam > Class 9 Questions > ABCD is a parallelogram. If the two diagonals... Start Learning for Free
ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?
- a)AAS
- b)SSS
- c)SAS
- d)RHS
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
ABCD is a parallelogram. If the two diagonals AC and BD are equal, the...
Proof of Congruence
1. Given:
Triangles ABD and ABC are congruent.
3. Explanation:
1. Given:
- ABCD is a parallelogram.
- Diagonals AC and BD are equal.
Triangles ABD and ABC are congruent.
3. Explanation:
- In a parallelogram, if the diagonals are equal, then the parallelogram is a rectangle because only rectangles have equal diagonals.
- Since ABCD is a rectangle, its diagonals bisect each other and are equal in length, meaning each half of the diagonal is also equal.
- In triangles ABD and ABC:
- AB is common to both triangles.
- BD = AC, as they are equal diagonals of the rectangle.
- AD = BC, as opposite sides of the rectangle are equal.
- Thus, by the SSS (Side-Side-Side) criterion, △ABD ≅ △ABC.
Free Test
FREE
| Start Free Test |
Community Answer
ABCD is a parallelogram. If the two diagonals AC and BD are equal, the...
Understanding the Parallelogram Properties
In parallelogram ABCD, diagonals AC and BD are equal in length, which is a special case. This characteristic leads us to analyze the triangles ABD and ABC for congruence.
Triangles in Consideration
- Triangle ABD: Formed by vertices A, B, and D.
- Triangle ABC: Formed by vertices A, B, and C.
Key Properties of the Parallelogram
- Opposite Sides: In a parallelogram, opposite sides are equal (AB = CD and AD = BC).
- Diagonals: Given that AC = BD, we can further analyze the triangles.
Criteria for Congruence
To determine the congruence of triangles ABD and ABC, we can use the Side-Side-Side (SSS) criterion:
- AB = AB: Common side.
- AD = BC: Opposite sides of the parallelogram.
- AC = BD: Given diagonals are equal.
Conclusion on Congruence
By the SSS criterion, we find that:
- Both triangles have equal corresponding sides.
- Therefore, triangle ABD is congruent to triangle ABC by the SSS criterion.
Why SSS is Applicable Here
- Each side of triangle ABD corresponds to a side of triangle ABC, establishing congruence.
- The equal diagonals (AC = BD) strengthen this criterion by ensuring all sides are accounted for.
In summary, triangles ABD and ABC are congruent by the SSS criterion, confirming the correct answer is option 'B'.
In parallelogram ABCD, diagonals AC and BD are equal in length, which is a special case. This characteristic leads us to analyze the triangles ABD and ABC for congruence.
Triangles in Consideration
- Triangle ABD: Formed by vertices A, B, and D.
- Triangle ABC: Formed by vertices A, B, and C.
Key Properties of the Parallelogram
- Opposite Sides: In a parallelogram, opposite sides are equal (AB = CD and AD = BC).
- Diagonals: Given that AC = BD, we can further analyze the triangles.
Criteria for Congruence
To determine the congruence of triangles ABD and ABC, we can use the Side-Side-Side (SSS) criterion:
- AB = AB: Common side.
- AD = BC: Opposite sides of the parallelogram.
- AC = BD: Given diagonals are equal.
Conclusion on Congruence
By the SSS criterion, we find that:
- Both triangles have equal corresponding sides.
- Therefore, triangle ABD is congruent to triangle ABC by the SSS criterion.
Why SSS is Applicable Here
- Each side of triangle ABD corresponds to a side of triangle ABC, establishing congruence.
- The equal diagonals (AC = BD) strengthen this criterion by ensuring all sides are accounted for.
In summary, triangles ABD and ABC are congruent by the SSS criterion, confirming the correct answer is option 'B'.
 | Explore Courses for Class 9 exam |  |
Top Courses for Class 9View all
Top Courses for Class 9
Question Description
ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer?.
ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer?.
Solutions for ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. 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 ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice ABCD is a parallelogram. If the two diagonals AC and BD are equal, then by what criterion are the triangles ABD and ABC congruent?a) AASb) SSSc) SASd) RHSCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 9 tests.
| Explore Courses for Class 9 exam | |
Top Courses for Class 9
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
