Geometry Chapter 5 Flashcards
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Questions and Answers

What does the Triangle Midsegment Theorem state?

  • The segment is equal to the third side.
  • The segment is parallel to the third side. (correct)
  • The segment is twice as long as the third side.
  • The segment is perpendicular to the third side.

    • What is a Midsegment in a triangle?

    Segment connecting the midpoints of two sides of a triangle.

    What does the term Equidistant mean?

    Equal distance away from two objects.

    What does the Perpendicular Bisector Theorem imply?

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

    What does the Converse of the Perpendicular Bisector Theorem state?

    <p>A point equidistant from the endpoints lies on the perpendicular bisector.</p> Signup and view all the answers

    What is the Angle Bisector Theorem?

    <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 Angle Bisector Theorem indicate?

    <p>Being equidistant from the angle sides means it’s on the bisector.</p> Signup and view all the answers

    What does Concurrent mean?

    <p>When three or more lines intersect at one point.</p> Signup and view all the answers

    What is a Point of Concurrency?

    <p>The point at which three or more lines intersect.</p> Signup and view all the answers

    What is a Circumcenter?

    <p>The point of concurrency of the perpendicular bisectors of a triangle.</p> Signup and view all the answers

    What does Circumscribe mean in reference to a triangle?

    <p>The circle that is around the triangle touching all points (vertices).</p> Signup and view all the answers

    What is an Incenter?

    <p>The point of concurrency of the angle bisectors of a triangle.</p> Signup and view all the answers

    What does Inscribe mean?

    <p>The circle that is inside the triangle.</p> Signup and view all the answers

    What is a Median in a triangle?

    <p>A segment whose endpoints are a vertex and the midpoint of the opposite side.</p> Signup and view all the answers

    What is a Centroid?

    <p>The point of concurrency of the medians.</p> Signup and view all the answers

    What is an Altitude in a triangle?

    <p>The perpendicular segment from a vertex of the triangle to the line containing the opposite side.</p> Signup and view all the answers

    What is an Orthocenter?

    <p>The point of concurrency of the altitudes.</p> Signup and view all the answers

    What is an Angle Bisector?

    <p>A ray that divides an angle into two congruent angles.</p> Signup and view all the answers

    What is a Perpendicular Bisector?

    <p>A line, segment, or ray that is perpendicular to the segment at its midpoint.</p> Signup and view all the answers

    Study Notes

    Triangle Midsegment Theorem

    • A segment that connects the midpoints of two sides of a triangle is parallel to the third side.
    • This segment measures half the length of the third side.

    Midsegment

    • Defined as the segment that joins the midpoints of two sides of a triangle.

    Equidistant

    • Refers to being equal distance from two objects or points.

    Perpendicular Bisector Theorem

    • A point located on the perpendicular bisector of a line segment is equidistant from the segment's endpoints.

    Converse of the Perpendicular Bisector Theorem

    • If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of that segment.

    Angle Bisector Theorem

    • A point on the bisector of an angle is equidistant from the angle’s sides.

    Converse of Angle Bisector Theorem

    • A point within the interior of an angle that is equidistant from the angle's sides lies on the angle bisector.

    Concurrent

    • Describes a scenario where three or more lines intersect at a single point.

    Point of Concurrency

    • The specific point where three or more lines intersect.

    Circumcenter

    • The point of concurrency formed by the perpendicular bisectors of a triangle.

    Circumscribe

    • Refers to a circle that surrounds a triangle and touches all its vertices.

    Incenter

    • The point of concurrency of the angle bisectors in a triangle.

    Inscribe

    • A circle that is contained within a triangle, touching all sides.

    Median

    • A segment that connects a vertex of a triangle to the midpoint of the opposite side.

    Centroid

    • The point where the medians of a triangle intersect.

    Altitude

    • The perpendicular segment drawn from a vertex of a triangle to the line containing the opposite side.

    Orthocenter

    • The point of concurrency formed by the altitudes of a triangle.

    Angle Bisector

    • A ray that divides an angle into two equal (congruent) angles.

    Perpendicular Bisector

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

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    Test your knowledge of the key terms and concepts from Geometry Chapter 5 with these flashcards. Each card features a term along with its definition, including important theorems related to triangles and segments. Enhance your understanding of geometric principles!

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