Class 10 Exam > Class 10 Questions > Points P, Q and R lie on sides BC, CA and AB ...
Start Learning for Free
Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.?
Most Upvoted Answer
Points P, Q and R lie on sides BC, CA and AB respectively of triangle ...
Proof:
Given: Triangle ABC with points P, Q and R on sides BC, CA and AB respectively such that PQ||AB and QR||BC.
To prove: RP||CA.
Proof:
Step 1: Draw a diagram of the given triangle ABC with points P, Q and R on sides BC, CA and AB respectively such that PQ||AB and QR||BC.
Step 2: Draw a line segment from point R to point C.
Step 3: Since PQ||AB and QR||BC, we have ∠QRC = ∠ABC and ∠PQR = ∠BAC (corresponding angles).
Step 4: Also, since RP is a transversal cutting parallel lines BC and PQ, we have ∠RPA = ∠PQC (alternate angles).
Step 5: Adding ∠QRC and ∠RPA, we get:
∠QRC + ∠RPA = ∠ABC + ∠PQC (using corresponding angles)
Step 6: Simplifying the above equation, we get:
∠QRP = ∠ACB
Step 7: Since ∠QRP and ∠ACB are alternate interior angles, we have RP||CA.
Step 8: Therefore, RP||CA is proved.
Conclusion: Hence, it is proved that RP||CA in the given triangle ABC with points P, Q and R on sides BC, CA and AB respectively such that PQ||AB and QR||BC.
Given: Triangle ABC with points P, Q and R on sides BC, CA and AB respectively such that PQ||AB and QR||BC.
To prove: RP||CA.
Proof:
Step 1: Draw a diagram of the given triangle ABC with points P, Q and R on sides BC, CA and AB respectively such that PQ||AB and QR||BC.
Step 2: Draw a line segment from point R to point C.
Step 3: Since PQ||AB and QR||BC, we have ∠QRC = ∠ABC and ∠PQR = ∠BAC (corresponding angles).
Step 4: Also, since RP is a transversal cutting parallel lines BC and PQ, we have ∠RPA = ∠PQC (alternate angles).
Step 5: Adding ∠QRC and ∠RPA, we get:
∠QRC + ∠RPA = ∠ABC + ∠PQC (using corresponding angles)
Step 6: Simplifying the above equation, we get:
∠QRP = ∠ACB
Step 7: Since ∠QRP and ∠ACB are alternate interior angles, we have RP||CA.
Step 8: Therefore, RP||CA is proved.
Conclusion: Hence, it is proved that RP||CA in the given triangle ABC with points P, Q and R on sides BC, CA and AB respectively such that PQ||AB and QR||BC.
Community Answer
Points P, Q and R lie on sides BC, CA and AB respectively of triangle ...
In triangle ABC PQ||AB =)AQ/QC=CP/PB----(1)(BPT) now QR||BC=) AR/RB=AQ/QC-----(2)(BPT) from(1) and(2) we get AR/RB=CP/PB=) RP||CA(converse of BPT)[proved]
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.?
Question Description
Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.?.
Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.?.
Solutions for Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? defined & explained in the simplest way possible. Besides giving the explanation of
Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.?, a detailed solution for Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? has been provided alongside types of Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? theory, EduRev gives you an
ample number of questions to practice Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ||AB and QR||BC, prove that RP||CA.? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 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