Geometry Chapter 5 Review Flashcards
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Questions and Answers

What is the definition of a median?

  • A line that divides an angle into two equal parts.
  • A segment from the vertex of the triangle to the opposite side.
  • A segment whose endpoints are in the vertex of the triangle and the midpoint of the opposite side. (correct)
  • A segment that connects two midpoints of a triangle.

    • What is a centroid?

    The point of concurrency for the three medians in a triangle.

    What does the centroid theorem state?

    The top half of the vertical line is $\frac{2}{3}$ of the lower portion of the vertical line.

    The centroid is always located inside the triangle.

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

    How does the centroid divide the median?

    <p>Into two parts with a ratio of 2:1.</p> Signup and view all the answers

    What is the definition of an altitude in a triangle?

    <p>Perpendicular segments from the vertex of a 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 three altitudes in a triangle.</p> Signup and view all the answers

    What defines a midsegment of a triangle?

    <p>A segment joining the midpoints of two sides of a triangle.</p> Signup and view all the answers

    The midsegment is half of the lower segment.

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

    What is a locus in geometry?

    <p>A set of points that satisfies a certain condition.</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 is the converse of the perpendicular bisector theorem?

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

    What are concurrent lines?

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

    What is a point of concurrency?

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

    What is a circumcenter?

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

    What does the circumcenter theorem state?

    <p>If circumcenter is the circumcenter of a triangle, then it is equidistant from the vertices.</p> Signup and view all the answers

    What is a circumscribed circle?

    <p>A circle that contains all the vertices of a polygon.</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 it is equidistant from the sides of the angle.</p> Signup and view all the answers

    What is the converse of the angle bisector theorem?

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

    What is an incenter?

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

    What does the incenter theorem state?

    <p>If incenter is the incenter of a triangle, then it is equidistant from the three sides of the triangle.</p> Signup and view all the answers

    What is an inscribed circle?

    <p>A circle inscribed in a polygon that intersects each side at exactly one point.</p> Signup and view all the answers

    What does the exterior angle inequality state?

    <p>The measure of the exterior angle is greater than either of its remote interior angles.</p> Signup and view all the answers

    What does the triangle inequality theorem state?

    <p>The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.</p> Signup and view all the answers

    What does the hinge theorem state?

    <p>If two sets of sides are congruent and included angles (hinges) are not congruent, then the larger hinged angle is across from the longer side.</p> Signup and view all the answers

    What is the converse of the hinge theorem?

    <p>If two sets of sides are congruent and the third sides are not, then the longer side is across from the larger hinged angle.</p> Signup and view all the answers

    Study Notes

    Median

    • A median connects a triangle's vertex to the midpoint of the opposite side.

    Centroid

    • The centroid is where the three medians of a triangle intersect.
    • It acts as the triangle's balancing point and is always located inside the triangle.

    Centroid Theorem

    • The segment created by a median is divided by the centroid into two sections, with the upper section measuring 2/3 of the total median length.

    Altitude

    • An altitude is a perpendicular segment from a triangle's vertex to the line containing the opposite side.

    Orthocenter

    • The point where the three altitudes of a triangle intersect is called the orthocenter.

    Midsegment

    • A midsegment connects the midpoints of two sides of the triangle and is half the length of the base segment it parallels.

    Locus

    • A locus is a collection of points that fulfill a specific condition.

    Perpendicular Bisector Theorem

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

    Converse of Perpendicular Bisector Theorem

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

    Concurrent Lines

    • Concurrent lines are three or more lines that meet at a single point, known as the point of concurrency.

    Circumcenter

    • The circumcenter is where the three perpendicular bisectors of a triangle intersect.

    Circumcenter Theorem

    • The circumcenter is equidistant from all vertices of the triangle.

    Circumscribed Circle

    • A circumcircle surrounds a polygon, touching all its vertices.

    Angle Bisector Theorem

    • A point on the bisector of an angle remains equidistant from the angle's sides.

    Converse of the Angle Bisector Theorem

    • If a point in the interior of an angle is equidistant from its sides, it must lie on the angle bisector.

    Incenter

    • The incenter is the intersection point of the three angle bisectors of a triangle.

    Incenter Theorem

    • The incenter is equidistant from all three sides of the triangle.

    Inscribed Circle

    • An inscribed circle touches each side of a polygon at exactly one point.

    Exterior Angle Inequality

    • An exterior angle of a triangle is greater than the measures of either of its remote interior angles.

    Triangle Inequality Theorem

    • For any triangle, the sum of lengths of any two sides must exceed the length of the third side.

    Hinge Theorem

    • If two sides are congruent but the included angles are not, the larger angle lies opposite the longer side.

    Converse of Hinge Theorem

    • If two sets of sides are congruent, the longer side is opposite the larger angle.

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    Description

    Test your knowledge of key concepts in Geometry Chapter 5 with these flashcards. This review covers important terms such as median, centroid, and centroid theorem, helping reinforce your understanding of triangle properties. Perfect for quick studying and revision.

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