Class 7 Exam > Class 7 Questions > In the figure , ABCD is a quadriletaral in wh...
Start Learning for Free
In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.?
Verified Answer
In the figure , ABCD is a quadriletaral in which AB is parallel to DC ...
Given=AB parallel to DC and AD parallel to BC
To Prove=Angle ADC=Angle ABC
Proof=
AB parallel to DC andAD parallel toBC so ABCD is a parallelogram and opposite angles of parallelogram are equal so angle ADC =angle ABC
This question is part of UPSC exam. View all Class 7 courses
Most Upvoted Answer
In the figure , ABCD is a quadriletaral in which AB is parallel to DC ...
Given:
- ABCD is a quadrilateral.
- AB is parallel to DC.
- AD is parallel to BC.
To prove:
Angle ADC = Angle ABC.
Proof:
Step 1: Identify the Opposite Angles.
- In the quadrilateral ABCD, identify the opposite angles.
- The opposite angles are ∠ADC and ∠CBA, and ∠DAB and ∠BCD.
Step 2: Identify the Corresponding Angles.
- Since AB is parallel to DC and AD is parallel to BC, corresponding angles are formed.
- Identify the corresponding angles in quadrilateral ABCD.
- The corresponding angles are ∠ADC and ∠CBA, and ∠DAB and ∠BCD.
Step 3: Use Corresponding Angles Theorem.
- According to the Corresponding Angles Theorem, if a transversal intersects two parallel lines, then the corresponding angles formed are congruent.
- In quadrilateral ABCD, ∠ADC and ∠CBA are corresponding angles and ∠ADC = ∠CBA.
Step 4: Conclude.
- From step 3, we know that ∠ADC = ∠CBA.
- Since ∠ADC = ∠CBA and ∠ADC is an opposite angle of ∠ABC, then ∠ABC = ∠CBA.
- Therefore, ∠ADC = ∠ABC.
Conclusion:
Therefore, it is proven that in the given quadrilateral ABCD, angle ADC is equal to angle ABC.
- ABCD is a quadrilateral.
- AB is parallel to DC.
- AD is parallel to BC.
To prove:
Angle ADC = Angle ABC.
Proof:
Step 1: Identify the Opposite Angles.
- In the quadrilateral ABCD, identify the opposite angles.
- The opposite angles are ∠ADC and ∠CBA, and ∠DAB and ∠BCD.
Step 2: Identify the Corresponding Angles.
- Since AB is parallel to DC and AD is parallel to BC, corresponding angles are formed.
- Identify the corresponding angles in quadrilateral ABCD.
- The corresponding angles are ∠ADC and ∠CBA, and ∠DAB and ∠BCD.
Step 3: Use Corresponding Angles Theorem.
- According to the Corresponding Angles Theorem, if a transversal intersects two parallel lines, then the corresponding angles formed are congruent.
- In quadrilateral ABCD, ∠ADC and ∠CBA are corresponding angles and ∠ADC = ∠CBA.
Step 4: Conclude.
- From step 3, we know that ∠ADC = ∠CBA.
- Since ∠ADC = ∠CBA and ∠ADC is an opposite angle of ∠ABC, then ∠ABC = ∠CBA.
- Therefore, ∠ADC = ∠ABC.
Conclusion:
Therefore, it is proven that in the given quadrilateral ABCD, angle ADC is equal to angle ABC.
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 the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.?
Question Description
In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? 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 the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.?.
In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? 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 the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.?.
Solutions for In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? 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 the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? defined & explained in the simplest way possible. Besides giving the explanation of
In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.?, a detailed solution for In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? has been provided alongside types of In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? theory, EduRev gives you an
ample number of questions to practice In the figure , ABCD is a quadriletaral in which AB is parallel to DC and AD is parallel to BC. prove that angle ADC = angle ABC.? 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup