Class 7 Exam > Class 7 Questions > PQR is a triangle in which PL is the bisector...
Start Learning for Free
PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles?
Most Upvoted Answer
PQR is a triangle in which PL is the bisector of angle QPR. If PL bise...
Proof that Triangle PQR is Isosceles
Given:
- Triangle PQR with PL bisecting angle QPR and QR
- PL is the bisector of angle QPR
Proof:
1. Angle Bisector Theorem
- By the Angle Bisector Theorem, we know that the bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
- In this case, PL bisects angle QPR, so it divides side QR into two segments (PQ and PR) that are proportional to sides PQ and PR.
2. Definition of Isosceles Triangle
- An isosceles triangle is a triangle in which at least two sides are congruent.
- If PL bisects QR, then PQ = PR (as they are proportional to each other).
- Therefore, sides PQ and PR are congruent in triangle PQR.
3. Conclusion
- Since we have shown that sides PQ and PR are congruent in triangle PQR, we can conclude that triangle PQR is an isosceles triangle.
Therefore, based on the given information and the Angle Bisector Theorem, we have proved that triangle PQR is an isosceles triangle.
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
PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles?
Question Description
PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? 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 PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles?.
PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? 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 PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles?.
Solutions for PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? 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 PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? defined & explained in the simplest way possible. Besides giving the explanation of
PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles?, a detailed solution for PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? has been provided alongside types of PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? theory, EduRev gives you an
ample number of questions to practice PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles? 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