Class 9 Exam > Class 9 Questions > In the adjacent figure ABCD is a parallelogra...
Start Learning for Free
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC?
Most Upvoted Answer
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle sho...
Community Answer
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle sho...
Understanding the Configuration
In the given configuration, we have a parallelogram ABCD and a rectangle ABEF. We need to show that triangles AFD and BEC are congruent.
Identifying Key Points
- Parallelogram Properties:
- Opposite sides are equal: AB = CD and AD = BC.
- Opposite angles are equal: ∠A = ∠C and ∠B = ∠D.
- Rectangle Properties:
- All angles are right angles: ∠ABE = ∠BAE = ∠EAF = ∠FEA = 90 degrees.
- Opposite sides are equal: AB = EF and AE = BF.
Triangles to Compare
- Triangle AFD:
- Vertices: A, F, D.
- Contains one right angle at F (since ABEF is a rectangle).
- Triangle BEC:
- Vertices: B, E, C.
- Also contains one right angle at E (since ABEF is a rectangle).
Proving Congruence
- Side Lengths:
- AF = BE (since both are sides of the rectangle).
- AD = BC (opposite sides of the parallelogram).
- Shared Side:
- The side FD is common to both triangles.
- Angle Criteria:
- ∠AFD = ∠BEC (both are right angles).
Conclusion
Using the Side-Angle-Side (SAS) Congruence Postulate:
1. AF = BE (equal sides).
2. FD is common.
3. ∠AFD = ∠BEC (both are right angles).
Thus, triangles AFD and BEC are congruent. This demonstrates that the properties of both the parallelogram and rectangle facilitate the congruence of the triangles, confirming the relationship effectively.
In the given configuration, we have a parallelogram ABCD and a rectangle ABEF. We need to show that triangles AFD and BEC are congruent.
Identifying Key Points
- Parallelogram Properties:
- Opposite sides are equal: AB = CD and AD = BC.
- Opposite angles are equal: ∠A = ∠C and ∠B = ∠D.
- Rectangle Properties:
- All angles are right angles: ∠ABE = ∠BAE = ∠EAF = ∠FEA = 90 degrees.
- Opposite sides are equal: AB = EF and AE = BF.
Triangles to Compare
- Triangle AFD:
- Vertices: A, F, D.
- Contains one right angle at F (since ABEF is a rectangle).
- Triangle BEC:
- Vertices: B, E, C.
- Also contains one right angle at E (since ABEF is a rectangle).
Proving Congruence
- Side Lengths:
- AF = BE (since both are sides of the rectangle).
- AD = BC (opposite sides of the parallelogram).
- Shared Side:
- The side FD is common to both triangles.
- Angle Criteria:
- ∠AFD = ∠BEC (both are right angles).
Conclusion
Using the Side-Angle-Side (SAS) Congruence Postulate:
1. AF = BE (equal sides).
2. FD is common.
3. ∠AFD = ∠BEC (both are right angles).
Thus, triangles AFD and BEC are congruent. This demonstrates that the properties of both the parallelogram and rectangle facilitate the congruence of the triangles, confirming the relationship effectively.
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
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC?
Question Description
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? 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 In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC?.
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? 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 In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC?.
Solutions for In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? 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 In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? defined & explained in the simplest way possible. Besides giving the explanation of
In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC?, a detailed solution for In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? has been provided alongside types of In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? theory, EduRev gives you an
ample number of questions to practice In the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that ∆AFD congruent to ∆BEC? 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup