Line l is the bisector of an angle ∠A and B is any point on it. If BP and BQ are

perpendiculars from B to the arms of ∠A, show that B is equidistant from the arms of

∠A.

Pleas draw diagram

Here is the diagram illustrating the angle \( \angle A \) with point \( B \) on the bisector and the perpendiculars \( BP \) and \( BQ \) drawn to the arms of the angle. This shows that point \( B \) is equidistant from the arms \( OP \) and \( OQ \).

If you have any questions or would like further clarification, feel free to ask!

Here are some related questions for further exploration:
1. What is the significance of the angle bisector in terms of distance?
2. How would the result change if \( B \) is not on the bisector?
3. Can we generalize this concept to three dimensions?
4. How can this result be applied in coordinate geometry?
5. What happens if \( BP \) and \( BQ \) are not perpendicular?

**Tip:** When solving geometry problems, always try to visualize the diagram to understand the relationships between elements.

Line l is the bisector of an angle ∠A and B is any point on it. If BP and BQ are perpendiculars from B to the arms of ∠A, show that B is equidistant from the arms of ∠A.

Explore the proof that a point on the bisector of an angle is equidistant from the arms of the angle. Using perpendicular distances and the Angle Bisector Theorem, this problem helps to solidify understanding of geometry concepts. Suitable for students in Grades 9-10.

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