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If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.?
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If two straight line intersect each other then prove that the opposite...
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If two straight line intersect each other then prove that the opposite...
Introduction
When two straight lines intersect, they form four angles. This scenario allows us to explore the relationship between angle bisectors and vertically opposite angles.
Angle Formation
- Let lines AB and CD intersect at point O.
- This results in angles AOC, AOD, BOC, and BOD.
Angle Bisector Definition
- An angle bisector divides an angle into two equal parts.
- Let the bisector of angle AOC be represented as line OE.
Proof of the Relationship
1. Equal Angles Formed:
- Since OE is the bisector of angle AOC, we have:
- Angle AOE = Angle EOC
2. Vertically Opposite Angles:
- By the properties of intersecting lines, we know:
- Angle AOC = Angle BOD (vertically opposite angles)
- Angle AOD = Angle BOC
3. Using Equal Angles:
- From the equality of angles:
- Angle AOC = Angle AOE + Angle EOC
- Substituting from the bisector:
- Angle AOC = 2 * Angle AOE
4. Implication for Vertically Opposite Angles:
- Since Angle BOD is also equal to Angle AOC, we can state:
- Angle BOD = 2 * Angle AOE
5. Conclusion:
- Thus, the bisector OE of angle AOC also bisects angle BOD, confirming that:
- Angle BOE = Angle EOD
Final Statement
- Therefore, the opposite bisector of the angles formed by two intersecting straight lines does indeed bisect the vertically opposite angle, proving our assertion.
When two straight lines intersect, they form four angles. This scenario allows us to explore the relationship between angle bisectors and vertically opposite angles.
Angle Formation
- Let lines AB and CD intersect at point O.
- This results in angles AOC, AOD, BOC, and BOD.
Angle Bisector Definition
- An angle bisector divides an angle into two equal parts.
- Let the bisector of angle AOC be represented as line OE.
Proof of the Relationship
1. Equal Angles Formed:
- Since OE is the bisector of angle AOC, we have:
- Angle AOE = Angle EOC
2. Vertically Opposite Angles:
- By the properties of intersecting lines, we know:
- Angle AOC = Angle BOD (vertically opposite angles)
- Angle AOD = Angle BOC
3. Using Equal Angles:
- From the equality of angles:
- Angle AOC = Angle AOE + Angle EOC
- Substituting from the bisector:
- Angle AOC = 2 * Angle AOE
4. Implication for Vertically Opposite Angles:
- Since Angle BOD is also equal to Angle AOC, we can state:
- Angle BOD = 2 * Angle AOE
5. Conclusion:
- Thus, the bisector OE of angle AOC also bisects angle BOD, confirming that:
- Angle BOE = Angle EOD
Final Statement
- Therefore, the opposite bisector of the angles formed by two intersecting straight lines does indeed bisect the vertically opposite angle, proving our assertion.
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If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.?
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If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.? 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 If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.?.
If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.? 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 If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two straight line intersect each other then prove that the opposite to the bisector of the angles so formed bisects the vertically opposite angle.?.
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