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In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that
1) OB = OC
2) AO bisects angle A?
1) OB = OC
2) AO bisects angle A?
Most Upvoted Answer
In an isosceles triangle ABC, with AB = AC ,the bisector of angle B an...
1. OB = OC
To show that OB = OC, we will use the property of angle bisectors in triangle ABC.
- Since AB = AC (isosceles triangle), we have:
- Angle B = Angle C (by the property of isosceles triangles)
- The angle bisector of angle B divides it into two equal angles:
- Angle OBA = Angle OBC
- Similarly, the angle bisector of angle C divides it into:
- Angle OCA = Angle OCB
- Since Angle OBA = Angle OCA and Angle OBC = Angle OCB, we can conclude that:
- Triangle OAB ≅ Triangle OAC (by the Angle-Side-Angle criterion)
- Therefore, the corresponding sides are equal:
- OB = OC
2. AO bisects angle A
To demonstrate that AO bisects angle A, we will analyze the angles formed by lines AO, OB, and OC.
- Since O is the intersection of the angle bisectors of angles B and C:
- Angle OAB + Angle OAC = Angle A
- We have established earlier that:
- Angle OBA = Angle OCA and Angle OBC = Angle OCB
- Thus, we can say:
- Angle OAB = Angle OAC (because both angles are opposite the equal sides OB and OC)
- Therefore, the angles are equal, leading to the conclusion that:
- AO bisects angle A
This confirms both properties, completing the proof that OB = OC and AO bisects angle A in triangle ABC.
To show that OB = OC, we will use the property of angle bisectors in triangle ABC.
- Since AB = AC (isosceles triangle), we have:
- Angle B = Angle C (by the property of isosceles triangles)
- The angle bisector of angle B divides it into two equal angles:
- Angle OBA = Angle OBC
- Similarly, the angle bisector of angle C divides it into:
- Angle OCA = Angle OCB
- Since Angle OBA = Angle OCA and Angle OBC = Angle OCB, we can conclude that:
- Triangle OAB ≅ Triangle OAC (by the Angle-Side-Angle criterion)
- Therefore, the corresponding sides are equal:
- OB = OC
2. AO bisects angle A
To demonstrate that AO bisects angle A, we will analyze the angles formed by lines AO, OB, and OC.
- Since O is the intersection of the angle bisectors of angles B and C:
- Angle OAB + Angle OAC = Angle A
- We have established earlier that:
- Angle OBA = Angle OCA and Angle OBC = Angle OCB
- Thus, we can say:
- Angle OAB = Angle OAC (because both angles are opposite the equal sides OB and OC)
- Therefore, the angles are equal, leading to the conclusion that:
- AO bisects angle A
This confirms both properties, completing the proof that OB = OC and AO bisects angle A in triangle ABC.
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In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that 1) OB = OC 2) AO bisects angle A?
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In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that 1) OB = OC 2) AO bisects angle A? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that 1) OB = OC 2) AO bisects angle A? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that 1) OB = OC 2) AO bisects angle A?.
In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that 1) OB = OC 2) AO bisects angle A? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that 1) OB = OC 2) AO bisects angle A? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an isosceles triangle ABC, with AB = AC ,the bisector of angle B and angle c intersect each other O .join A to O .show that 1) OB = OC 2) AO bisects angle A?.
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