Class 7 Exam > Class 7 Questions > in figure 9.9 it is given that AB=CD and AD=B...
Start Learning for Free
in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA
? Related: SSS Condition for Congruence
Most Upvoted Answer
in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Re...
**SSS Condition for Congruence**
The SSS condition for congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In other words, if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.
**Given Information**
In Figure 9.9, it is given that AB = CD and AD = BC. We need to prove that triangle ADC is similar to triangle CBA.
**Proof**
To prove that triangle ADC is similar to triangle CBA, we need to show that their corresponding sides are proportional and their corresponding angles are congruent.
**Corresponding Sides**
In this case, we have the following corresponding sides:
- AD corresponds to CB
- DC corresponds to AB
- AC corresponds to CA (common side)
We are given that AB = CD and AD = BC. From this information, we can see that the corresponding sides are equal in length.
**Corresponding Angles**
To show that the corresponding angles are congruent, we can use the fact that opposite sides in a parallelogram are parallel. Since AB is parallel to CD and AD is parallel to BC, we can conclude that angle ADC is congruent to angle CBA, and angle CDA is congruent to angle BAC.
**Conclusion**
Since the corresponding sides of triangle ADC and triangle CBA are equal in length, and their corresponding angles are congruent, we can conclude that triangle ADC is similar to triangle CBA based on the SSS condition for congruence.
Therefore, we have proved that triangle ADC is similar to triangle CBA.
The SSS condition for congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In other words, if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.
**Given Information**
In Figure 9.9, it is given that AB = CD and AD = BC. We need to prove that triangle ADC is similar to triangle CBA.
**Proof**
To prove that triangle ADC is similar to triangle CBA, we need to show that their corresponding sides are proportional and their corresponding angles are congruent.
**Corresponding Sides**
In this case, we have the following corresponding sides:
- AD corresponds to CB
- DC corresponds to AB
- AC corresponds to CA (common side)
We are given that AB = CD and AD = BC. From this information, we can see that the corresponding sides are equal in length.
**Corresponding Angles**
To show that the corresponding angles are congruent, we can use the fact that opposite sides in a parallelogram are parallel. Since AB is parallel to CD and AD is parallel to BC, we can conclude that angle ADC is congruent to angle CBA, and angle CDA is congruent to angle BAC.
**Conclusion**
Since the corresponding sides of triangle ADC and triangle CBA are equal in length, and their corresponding angles are congruent, we can conclude that triangle ADC is similar to triangle CBA based on the SSS condition for congruence.
Therefore, we have proved that triangle ADC is similar to triangle CBA.
Attention Class 7 Students!
To make sure you are not studying endlessly, EduRev has designed Class 7 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 7.
|
Explore Courses for Class 7 exam
|
|
Similar Class 7 Doubts
Top Courses for Class 7View all
in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence?
Question Description
in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence?.
in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence?.
Solutions for in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? in English & in Hindi are available as part of our courses for Class 7.
Download more important topics, notes, lectures and mock test series for Class 7 Exam by signing up for free.
Here you can find the meaning of in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? defined & explained in the simplest way possible. Besides giving the explanation of
in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence?, a detailed solution for in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? has been provided alongside types of in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? theory, EduRev gives you an
ample number of questions to practice in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? tests, examples and also practice Class 7 tests.
|
|
Explore Courses for Class 7 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