Class 9 Exam > Class 9 Questions > In a triangles ABC, D is a mistake point of B...
Start Learning for Free
In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC?
Most Upvoted Answer
In a triangles ABC, D is a mistake point of BC; AD is produced upto E ...
Community Answer
In a triangles ABC, D is a mistake point of BC; AD is produced upto E ...
Proof:
To prove the given statements, we will use the properties of congruent triangles and the fact that the opposite sides of a parallelogram are equal.
1) ∆ABD is congruent to ∆ECD:
Since DE = AD, we can conclude that ∆ADE is an isosceles triangle with DE = AD.
Now, in ∆ABD and ∆ECD, we can see that ∠ABD = ∠ECD (corresponding angles) and ∠BAD = ∠CDE (vertically opposite angles).
Since ∠ABD = ∠ECD and ∠BAD = ∠CDE, we can conclude that ∆ABD ≅ ∆ECD by the angle-side-angle (ASA) congruence criterion.
2) AB = EC:
Since ∆ABD ≅ ∆ECD, we can conclude that AD = ED (corresponding sides of congruent triangles).
Given that DE = AD, we can substitute AD for DE.
So, AD = AD, which implies that AD = AD.
Since AD = AD, we can conclude that AB = EC (opposite sides of a parallelogram are equal).
3) AB is parallel to EC:
Since AB = EC (proved in the previous step), and opposite sides of a parallelogram are parallel, we can conclude that AB is parallel to EC.
To summarize:
1) ∆ABD is congruent to ∆ECD.
2) AB = EC.
3) AB is parallel to EC.
Hence, the given statements have been proved using the properties of congruent triangles and the fact that opposite sides of a parallelogram are equal.
To prove the given statements, we will use the properties of congruent triangles and the fact that the opposite sides of a parallelogram are equal.
1) ∆ABD is congruent to ∆ECD:
Since DE = AD, we can conclude that ∆ADE is an isosceles triangle with DE = AD.
Now, in ∆ABD and ∆ECD, we can see that ∠ABD = ∠ECD (corresponding angles) and ∠BAD = ∠CDE (vertically opposite angles).
Since ∠ABD = ∠ECD and ∠BAD = ∠CDE, we can conclude that ∆ABD ≅ ∆ECD by the angle-side-angle (ASA) congruence criterion.
2) AB = EC:
Since ∆ABD ≅ ∆ECD, we can conclude that AD = ED (corresponding sides of congruent triangles).
Given that DE = AD, we can substitute AD for DE.
So, AD = AD, which implies that AD = AD.
Since AD = AD, we can conclude that AB = EC (opposite sides of a parallelogram are equal).
3) AB is parallel to EC:
Since AB = EC (proved in the previous step), and opposite sides of a parallelogram are parallel, we can conclude that AB is parallel to EC.
To summarize:
1) ∆ABD is congruent to ∆ECD.
2) AB = EC.
3) AB is parallel to EC.
Hence, the given statements have been proved using the properties of congruent triangles and the fact that opposite sides of a parallelogram are equal.
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
In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC?
Question Description
In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? 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 a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC?.
In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? 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 a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC?.
Solutions for In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? 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 a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? defined & explained in the simplest way possible. Besides giving the explanation of
In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC?, a detailed solution for In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? has been provided alongside types of In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? theory, EduRev gives you an
ample number of questions to practice In a triangles ABC, D is a mistake point of BC; AD is produced upto E so that DE=AD. Prove that: 1) ∆ABD is congruent to ∆ ECD 2) AB=EC 3) AB is parallel to EC? 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