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PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles?
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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.
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PQR is a triangle in which PL is the bisector of angle QPR. If PL bisects QR, show that triangle PQR is isosceles?
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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?.
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