Perpendicular Bisector and Angle Bisector Theorem

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What is a perpendicular bisector?

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A perpendicular bisector is a line that divides a line segment into two equal parts at a 90-degree angle.

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State the Perpendicular Bisector Theorem.

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The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

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What is an angle bisector?

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An angle bisector is a line or ray that divides an angle into two equal angles.

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State the Angle Bisector Theorem.

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The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

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How do you find the length of a segment using the Perpendicular Bisector Theorem?

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To find the length of a segment using the Perpendicular Bisector Theorem, measure the distance from any point on the bisector to each endpoint of the segment; these distances will be equal.

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What is the relationship between angles formed by an angle bisector?

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What is the significance of the point where the perpendicular bisector intersects a segment?

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The intersection point is the midpoint of the segment, and it is equidistant from both endpoints.

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