Geometry Chapter 5 Test Flashcards
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Questions and Answers

What is the median of a triangle?

  • A segment that joins a vertex to the midpoint of the opposite side (correct)
  • A quadrilateral with both pairs of opposite sides parallel
  • The point where the three medians intersect
  • A line that is perpendicular to a segment

    • What is the centroid of a triangle?

    The point of intersection of the three medians.

    Concurrent lines intersect in more than one point.

    False

    What is an altitude of a triangle?

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

    What is the definition of orthocenter?

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

    What is a perpendicular bisector?

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

    What is a circumcenter?

    <p>The point where the three perpendicular bisectors of the sides of a triangle meet.</p> Signup and view all the answers

    What does it mean to circumscribe a circle about a polygon?

    <p>All the vertices of the polygon lie on the circle.</p> Signup and view all the answers

    What is an angle bisector?

    <p>The segment that divides an angle of a triangle into two congruent angles.</p> Signup and view all the answers

    What is the incenter of a triangle?

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

    What does inscribed mean in geometry?

    <p>If a circle is inscribed in a polygon, it is tangent to each side of the polygon.</p> Signup and view all the answers

    What is a parallelogram?

    <p>A quadrilateral with both pairs of opposite sides parallel.</p> Signup and view all the answers

    What is a midline in a triangle?

    <p>The segment that joins the midpoints of two sides of a triangle.</p> Signup and view all the answers

    What defines a rectangle?

    <p>A quadrilateral with 4 right angles.</p> Signup and view all the answers

    What is a rhombus?

    <p>A quadrilateral with 4 congruent sides.</p> Signup and view all the answers

    What defines a square?

    <p>A quadrilateral with 4 congruent sides and 4 right angles.</p> Signup and view all the answers

    What is a trapezoid?

    <p>A quadrilateral with exactly one pair of sides parallel.</p> Signup and view all the answers

    What is an isosceles trapezoid?

    <p>A trapezoid with congruent legs.</p> Signup and view all the answers

    What do you call the parallel sides of a trapezoid?

    <p>Bases.</p> Signup and view all the answers

    What defines the legs of a trapezoid?

    <p>The two opposite sides of a trapezoid that are not parallel.</p> Signup and view all the answers

    What is the median of a trapezoid?

    <p>The segment that joins the midpoints of two legs of the trapezoid.</p> Signup and view all the answers

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

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

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

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

    If a point lies on the bisector of an angle, then it is equidistant from the sides of the angle.

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

    If a point is equidistant from the sides of an angle, then it lies on the bisector of the angle.

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

    Opposite sides of a parallelogram are not congruent.

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

    Diagonals of a parallelogram do not bisect each other.

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

    What is the converse of the theorem stating that if both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram?

    <p>If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.</p> Signup and view all the answers

    What does it mean if one pair of opposite sides of a quadrilateral are both congruent and parallel?

    <p>Then the quadrilateral is a parallelogram.</p> Signup and view all the answers

    If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.

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

    If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

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

    If two lines are parallel, then all points on one line are equidistant from the other line.

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

    What is the Venetian Blind Theorem?

    <p>If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.</p> Signup and view all the answers

    What is the Side Splitter Theorem?

    <p>A line that contains the midpoint of the side of a triangle and is parallel to another side passes through the midpoint of the third side.</p> Signup and view all the answers

    What is the Midline Theorem?

    <p>The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half its length.</p> Signup and view all the answers

    The diagonals of a rectangle are congruent.

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

    The diagonals of a rhombus are perpendicular.

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

    Each diagonal of a rhombus bisects two angles of the rhombus.

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

    What is the relationship of the midpoint of the hypotenuse of a right triangle to its vertices?

    <p>The midpoint is equidistant from the three vertices.</p> Signup and view all the answers

    If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.

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

    If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

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

    Base angles of an isosceles trapezoid are not congruent.

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

    What is the median of a trapezoid?

    <p>The median is parallel to the bases and has a length equal to the average of the bases.</p> Signup and view all the answers

    Study Notes

    Triangle Properties

    • Median: Segment connecting a vertex to the midpoint of the opposite side.
    • Centroid: Intersection point of medians, divides each median into segments with a 2:1 ratio; acts as the triangle's center of gravity.
    • Altitude: Perpendicular segment from a vertex to the line containing the opposite side.
    • Orthocenter: Concurrency point of the three altitudes in a triangle.

    Perpendicular and Bisector Concepts

    • Perpendicular Bisector: Line or segment that intersects another segment at its midpoint at a right angle.
    • Circumcenter: Meeting point of the three perpendicular bisectors; center of the circle circumscribing the triangle.
    • Angle Bisector: Segment that divides an angle into two equal angles.
    • Incenter: Concurrency point of angle bisectors; center of the inscribed circle that touches all sides.

    Polygon Definitions

    • Circumscribes: A circle surrounding a polygon where all vertices lie on the circle.
    • Inscribed: A circle that touches each side of a polygon at exactly one point.
    • Parallelogram: Quadrilateral with both pairs of opposite sides parallel.
    • Quadrilateral Types:
      • Rectangle: Four right angles.
      • Rhombus: Four congruent sides.
      • Square: Four congruent sides and four right angles.
      • Trapezoid: Quadrilateral with exactly one pair of parallel sides.
      • Isosceles Trapezoid: A trapezoid with congruent non-parallel sides.

    Trapezoid Features

    • Bases: The parallel sides of a trapezoid.
    • Legs: The non-parallel sides of a trapezoid.
    • Median of a Trapezoid: Segment connecting midpoints of the legs; parallel to the bases and averages their lengths.

    Perpendicular Bisector Theorems

    • 4.5 (PBT): A point on the perpendicular bisector is equidistant from segment endpoints.
    • 4.6 (CPBT): A point equidistant from segment endpoints lies on the perpendicular bisector.

    Angle Bisector Theorems

    • 4.7 (PBES): A point on the angle bisector is equidistant from the angle sides.
    • 4.8 (CPBES): A point equidistant from the sides of an angle lies on its bisector.

    Parallelogram Properties

    • 5.1 (OSC): Opposite sides are congruent.
    • 5.2 (OAC): Opposite angles are congruent.
    • 5.3 (DB): Diagonal bisectors intersect at their midpoints.
    • 5.4 (Converse of OSC→P): Quadrilateral with congruent opposite sides is a parallelogram.
    • 5.5 (OPCP): If one pair of sides is both congruent and parallel, it's a parallelogram.
    • 5.6 (Converse of OAC→P): Quadrilateral with congruent opposite angles is a parallelogram.
    • 5.7 (DB→P): If diagonals bisect each other, it's a parallelogram.

    Additional Theorems

    • 5.8 (PLEA): All points on one line are equidistant from a parallel line.
    • 5.9 (VBT): If multiple parallel lines cut congruent segments on one transversal, they do so on others.
    • 5.10 (SS): A line through the midpoint of one side, parallel to another, passes through the third side's midpoint.
    • 5.11 (Midline theorem): Segment joining midpoints of two sides is parallel to the third side and half its length.

    Rectangles and Rhombuses

    • 5.12 (DRC): Diagonals of a rectangle are congruent.
    • 5.13 (DRhP): Diagonals of a rhombus are perpendicular.
    • 5.14 (DRhBA): Each diagonal bisects two angles of the rhombus.

    Right Triangles and Parallelograms

    • 5.15 (MHRT): Midpoint of the hypotenuse in a right triangle is equidistant from all triangle vertices.
    • 5.16 (PRR): If an angle in a parallelogram is right, the parallelogram is a rectangle.
    • 5.17 (CSC): If two consecutive sides of a parallelogram are congruent, it is a rhombus.

    Isosceles Trapezoid Properties

    • 5.18 (BAIT): Base angles of an isosceles trapezoid are congruent.
    • 5.19 (MT): Median of a trapezoid is parallel to the bases, with a length equal to the average of the bases.

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    Test your knowledge of key concepts in Geometry Chapter 5 with these flashcards. Learn terms such as Median, Centroid, and Concurrent lines, and understand their importance in triangle properties. Ideal for students preparing for exams or seeking to reinforce their understanding of geometric principles.

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