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P is a point equidistant from two lines l and m intersecting at point A, then
- a)∠BAP = ∠APC
- b)∠CAP = ∠BPA
- c)∠CAP = ∠BAP
- d)None of there
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
P is a point equidistant from two lines l and m intersecting at point ...
In Δs ABP and ACP
PC = PB (Given)
∠ACP = ∠ABP = 90°
AP = AP (common)
∴ ΔABP ≅ ΔACP
(By R-H-S congruence criterion)
⇒ ∠BAP = ∠CAP (C.P.C.T)
PC = PB (Given)
∠ACP = ∠ABP = 90°
AP = AP (common)
∴ ΔABP ≅ ΔACP
(By R-H-S congruence criterion)
⇒ ∠BAP = ∠CAP (C.P.C.T)
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P is a point equidistant from two lines l and m intersecting at point ...
Understanding the Geometry of Point P
When a point P is equidistant from two intersecting lines l and m at point A, it creates specific angles that relate to point P and the lines.
Key Concepts
- Equidistant Definition: Point P being equidistant from lines l and m means that the perpendicular distances from P to both lines are equal.
- Intersection at Point A: The lines l and m intersect at point A, creating angles around A.
Angles Formed by Point P
- Angle Relationships: The angles formed at point A can be expressed in terms of P:
- Angle BAP is the angle between line l and line segment AP.
- Angle CAP is the angle between line m and line segment AP.
- Angle BPA is the angle between line l and line segment BP.
Reasoning for the Correct Answer
- Since P is equidistant from lines l and m, the angles formed with respect to A will have specific relationships:
- Angle CAP = Angle BAP: This is true because both angles are subtended by the same line segment AP from point P, making them equal.
- Angle CAP does not equal Angle BPA: These angles are not directly related as they involve different line segments and points.
Conclusion
Thus, the correct answer is option 'C':
Angle CAP = Angle BAP.
This equality arises due to the symmetry created by point P being equidistant from both lines.
When a point P is equidistant from two intersecting lines l and m at point A, it creates specific angles that relate to point P and the lines.
Key Concepts
- Equidistant Definition: Point P being equidistant from lines l and m means that the perpendicular distances from P to both lines are equal.
- Intersection at Point A: The lines l and m intersect at point A, creating angles around A.
Angles Formed by Point P
- Angle Relationships: The angles formed at point A can be expressed in terms of P:
- Angle BAP is the angle between line l and line segment AP.
- Angle CAP is the angle between line m and line segment AP.
- Angle BPA is the angle between line l and line segment BP.
Reasoning for the Correct Answer
- Since P is equidistant from lines l and m, the angles formed with respect to A will have specific relationships:
- Angle CAP = Angle BAP: This is true because both angles are subtended by the same line segment AP from point P, making them equal.
- Angle CAP does not equal Angle BPA: These angles are not directly related as they involve different line segments and points.
Conclusion
Thus, the correct answer is option 'C':
Angle CAP = Angle BAP.
This equality arises due to the symmetry created by point P being equidistant from both lines.
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