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?
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Orthocenter is formed by what?
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What is the point of concurrency?
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What does concurrent mean?
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What is an angle bisector?
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What is a perpendicular bisector?
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What is an altitude?
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What is a median?
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What does the Triangle Midsegment Theorem state?
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What does the Perpendicular Bisector Theorem state?
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What does the Converse of the Perpendicular Bisector Theorem state?
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What does the Angle Bisector Theorem state?
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What does the Converse of the Angle Bisector Theorem state?
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What does the Concurrency of Medians Theorem state?
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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.
Theorems Related to Triangles
- 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.
