Perpendicular bisector theorem

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What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

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How can 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, you can use the property that any point on the bisector is equidistant from the segment's endpoints.

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What does it mean for a line to be a perpendicular bisector?

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

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If point H is on the perpendicular bisector of segment FG, what can be said about the distances HF and HG?

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If point H is on the perpendicular bisector of segment FG, then HF = HG.

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How do you apply the Perpendicular Bisector Theorem to find unknown lengths in a triangle?

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To apply the Perpendicular Bisector Theorem in a triangle, identify the perpendicular bisector of a side and use the properties of the triangle to find unknown lengths.

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What is the relationship between the lengths of segments created by a perpendicular bisector?

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The lengths of the segments created by a perpendicular bisector are equal to each other.

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In a triangle, if a point lies on the perpendicular bisector of one side, what can be concluded about its distances to the other two vertices?

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The point is equidistant from the two vertices of the triangle that are endpoints of the side.

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How can the Perpendicular Bisector Theorem be used to solve for variables in geometric problems?

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The Perpendicular Bisector Theorem can be used to set up equations based on the equality of distances from a point on the bisector to the endpoints of the segment.

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What is the significance of the point where the perpendicular bisectors of a triangle intersect?

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The point where the perpendicular bisectors of a triangle intersect is called the circumcenter, which is equidistant from all three vertices of the triangle.

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How do you determine if a point is on the perpendicular bisector of a segment?

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To determine if a point is on the perpendicular bisector of a segment, check if it is equidistant from the endpoints of the segment.