Geometry Chapter 5 Review Flashcards
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Questions and Answers

Name the 4 points of concurrency.

Circumcenter, incenter, centroid, and orthocenter.

Circumcenter is formed by what?

Perpendicular Bisectors

Incenter is formed by what?

Angle Bisectors

Centroid is formed by what?

<p>Medians</p> Signup and view all the answers

Orthocenter is formed by what?

<p>Altitudes</p> Signup and view all the answers

What is the point of concurrency?

<p>The point where 3 or more lines intersect.</p> Signup and view all the answers

What does concurrent mean?

<p>Lines that intersect at one point.</p> Signup and view all the answers

What is an angle bisector?

<p>Drawn from a vertex; divides an angle into congruent angles.</p> Signup and view all the answers

What is a perpendicular bisector?

<p>Drawn from a midpoint of a side at a right angle.</p> Signup and view all the answers

What is an altitude?

<p>Drawn from a vertex to the opposite side at a right angle.</p> Signup and view all the answers

What is a median?

<p>Drawn from a vertex to the midpoint of the opposite side.</p> Signup and view all the answers

What does the Triangle Midsegment Theorem state?

<p>If a segment joins the midpoint of two sides of a triangle, then the segment is parallel to the third side and is half as long.</p> Signup and view all the answers

What does the Perpendicular Bisector Theorem state?

<p>If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.</p> Signup and view all the answers

What does the Converse of the Perpendicular Bisector Theorem state?

<p>If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of a segment.</p> Signup and view all the answers

What does the Angle Bisector Theorem state?

<p>If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.</p> Signup and view all the answers

What does the Converse of the Angle Bisector Theorem state?

<p>If a point in the interior of an angle is equidistant from the sides of an angle, then the point is on the angle bisector.</p> Signup and view all the answers

What does the Concurrency of Medians Theorem state?

<p>The medians of a triangle are concurrent at a point that is 2/3 the distance from each vertex to the midpoint of the opposite side.</p> Signup and view all the answers

Study Notes

Points of Concurrency

  • Four key points of concurrency: Circumcenter, Incenter, Centroid, and Orthocenter.
  • Circumcenter is formed by the intersection of Perpendicular Bisectors of the sides of a triangle.
  • Incenter is created by the intersection of Angle Bisectors, representing equal distance to the triangle's sides.
  • Centroid is formed by the intersection of Medians, which connect a vertex to the midpoint of the opposite side.
  • Orthocenter is defined by the intersection of Altitudes, lines drawn from a vertex perpendicular to the opposite side.

Definitions and Concepts

  • A Point of Concurrency is where three or more lines intersect.
  • Lines that meet at a single location are termed Concurrent.

Types of Lines in Triangles

  • An Angle Bisector divides an angle into two equal angles, originating from a vertex.
  • A Perpendicular Bisector is a line that intersects a segment at its midpoint at a right angle.
  • An Altitude extends from a vertex to the opposite side, forming a right angle with that side.
  • A Median connects a vertex to the midpoint of the opposing side.
  • Triangle Midsegment Theorem: A segment connecting midpoints of two sides is parallel to the third side, and its length is half that of the third side.
  • Perpendicular Bisector Theorem: A point on the perpendicular bisector of a segment is equidistant from both endpoints of that segment.
  • Converse of the Perpendicular Bisector Theorem: If a point is equidistant from the endpoints of a segment, it lies on the segment's perpendicular bisector.
  • Angle Bisector Theorem: A point on the bisector of an angle is equidistant from the sides of the angle.
  • Converse of the Angle Bisector Theorem: If a point inside an angle is equidistant from the angle's sides, it is located on the angle bisector.
  • Concurrency of Medians Theorem: The intersection of the medians occurs at a point that is two-thirds of the distance from each vertex to the midpoint of the opposite side.

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Description

Test your knowledge of Chapter 5 in Geometry with these flashcards. The quiz focuses on points of concurrency such as the circumcenter, incenter, centroid, and orthocenter, including how each is formed. Perfect for reinforcing key concepts and definitions.

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