Geometry Sections 5.1 and 5.2

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GeometrySections 5.1 and 5.2

• Midsegment Theorem
• Use Perpendicular Bisectors

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Midsegment of a triangle

• A segment that connects the midpoints of two
  sides of the triangle.
• Every triangle has 3 midsegments

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Midsegment Theorem

• The segment connecting the midpoints of two sides
  of a triangle is parallel to the third side and
  half as long as that side.

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Perpendicular bisector

• A segment, ray, line, or plane that is
  perpendicular to a segment at its midpoint.

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Perpendicular Bisector Theorem

• In a plane, if a point is on the perpendicular
  bisector of a segment, then it is equidistant
  (same distance) from the endpoints of the
  segment.

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Converse of the Perpendicular Bisector Theorem

• In a plane, if a point is equidistant from the
  endpoints of a segment, then it is on the
  perpendicular bisector of the segment

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Concurrency

• When three or more lines, rays, or segments
  intersect in the same point, they are called
  concurrent.
• The intersection of the lines, rays, or segments
  is the point of concurrency.

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Concurrency of Perpendicular Bisectors of a
Triangle

• The perpendicular bisectors of a triangle
  intersect at a point that is equidistant from the
  vertices of the triangle

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Circumcenter of a triangle

• The point of concurrency of the three
  perpendicular bisectors of a triangle.
• The circumcenter is equidistant from the three
  vertices, so it is the center of a circle that
  passes through all three vertices.

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Examples

• Power Point Examples

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Assignment

• Section 5.1
• Page 298
• Problems 3-10
• Section 5.2
• Page 306
• Problems 4-8, 11-16