Geometry Key Terms Quiz
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Geometry Key Terms Quiz

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Questions and Answers

What is a secant in relation to a circle?

  • A line that intersects a circle in exactly one point.
  • A line that intersects a circle in exactly two points. (correct)
  • A line that touches a circle at one point.
  • A line that passes through the center of the circle.

    • An inscribed angle is formed by two chords that do not share an endpoint on the circle.

    False

    Define a major arc.

    An arc of a circle that is greater than 180 degrees.

    A __________ is the center of the circle that is circumscribed about a polygon.

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

    Match the following angles with their definitions:

    <p>Exterior angle = An angle formed by one side of a polygon and the extension of an adjacent side. Remote interior angles = The two interior angles of a polygon that are not adjacent to a given exterior angle. Base angles = The two angles formed by the base of an isosceles triangle. Altitude = A perpendicular segment from a vertex of a triangle to the opposite side.</p> Signup and view all the answers

    What is the relationship between a chord and a tangent?

    <p>A tangent intersects at exactly one point, while a chord intersects at two points.</p> Signup and view all the answers

    A kite is defined as a quadrilateral with two pairs of adjacent sides that are not congruent.

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

    What is a postulate?

    <p>A statement accepted as true without proof.</p> Signup and view all the answers

    The __________ is the point where the altitudes of a triangle intersect.

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

    Which statement correctly describes a cyclic quadrilateral?

    <p>A quadrilateral whose vertices all lie on a circle.</p> Signup and view all the answers

    Which of the following is a characteristic of convex quadrilaterals?

    <p>All interior angles must be less than 180°</p> Signup and view all the answers

    A kite can only be classified if the diagonals are perpendicular and non-congruent.

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

    What term describes a line segment that connects non-adjacent vertices of a polygon?

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

    A concave quadrilateral has at least one angle greater than ______.

    <p>180°</p> Signup and view all the answers

    Match the types of quadrilaterals to their characteristics:

    <p>Rectangle = Four congruent angles Parallelogram = Opposite sides are equal and parallel Rhombus = All sides are equal Kite = Two pairs of equal adjacent sides</p> Signup and view all the answers

    What is a conjecture?

    <p>A mathematical function that hasn't been proven</p> Signup and view all the answers

    Vertical angles are always congruent.

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

    What is the sum of the measures of angles in a linear pair?

    <p>180°</p> Signup and view all the answers

    An inscribed angle has its vertex on a _____ and its sides contain chords of the circle.

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

    Match the following terms with their definitions:

    <p>Theorem = A statement that can be proven Postulate = A statement that is accepted as true without proof Inscribed Angle = An angle whose vertex is on a circle Circumscribed Angle = An angle with its sides tangent to the circle</p> Signup and view all the answers

    Which property is true for an isosceles trapezoid?

    <p>Only one pair of opposite angles is congruent.</p> Signup and view all the answers

    A parallelogram has only one pair of opposite sides that are parallel.

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

    What shape has all sides congruent?

    <p>Rhombus or Square</p> Signup and view all the answers

    In an isosceles trapezoid, the lengths of the _____ are congruent.

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

    Which of the following shapes has diagonals that are perpendicular?

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

    Match the following shapes with their specific properties:

    <p>Parallelogram = Opposite sides are parallel Rectangle = All angles are right angles Rhombus = All sides are congruent Kite = Diagonals are perpendicular</p> Signup and view all the answers

    A rectangle is a type of trapezoid.

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

    What is the key distinguishing feature of an isosceles trapezoid?

    <p>Congruent legs</p> Signup and view all the answers

    What is a midsegment of a polygon?

    <p>A line connecting the midpoints of two sides</p> Signup and view all the answers

    The opposite angles of a cyclic quadrilateral are never supplementary.

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

    What forms the vertex angle in an isosceles triangle?

    <p>The two congruent sides.</p> Signup and view all the answers

    A quadrilateral can be divided into two triangles by drawing a __________.

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

    Match the following geometric terms with their definitions:

    <p>Midsegment = Connects two midpoints of the polygon sides Cyclic quadrilateral = Vertices lie on a single circle Biconditional statement = True in both original and converse forms Hypothesis = The 'if' part of a conditional statement</p> Signup and view all the answers

    Which statement is a biconditional statement?

    <p>A polygon has three sides if and only if it is a triangle.</p> Signup and view all the answers

    The midsegment of a trapezoid is always parallel to its bases.

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

    In an isosceles triangle, the angles between the base and the congruent sides are called __________.

    <p>base angles</p> Signup and view all the answers

    What is true about the sum of the interior angles of a triangle?

    <p>It equals 180 degrees.</p> Signup and view all the answers

    The circumcenter of a triangle is not equidistant from the vertices.

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

    What is the relationship between an exterior angle and remote interior angles in a triangle?

    <p>The measure of the exterior angle is equal to the sum of the measures of the two remote interior angles.</p> Signup and view all the answers

    The midsegment of a triangle is ______ the measure and parallel to the third side.

    <p>one half of</p> Signup and view all the answers

    Match each term with its definition:

    <p>Circumscribed Circle = A circle that passes through all the vertices of a polygon. Point of Concurrency = The point at which concurrent lines intersect. Circumcenter = The point where the perpendicular bisectors of a triangle intersect. Remote Interior Angles = The two interior angles not adjacent to a specified exterior angle.</p> Signup and view all the answers

    What is the point of concurrency of the three angle bisectors of a triangle called?

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

    The centroid is the point of concurrency of the three angle bisectors of a triangle.

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

    What is the relationship between the distances from the centroid to the vertex and to the midpoint of the opposite side?

    <p>The distance from the centroid to the vertex is twice the distance from the centroid to the midpoint.</p> Signup and view all the answers

    The __________ is the point of concurrency of the three altitudes of a triangle.

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

    Match the following points of concurrency with their properties:

    <p>Incenter = Equidistant from all sides Circumcenter = Equidistant from all vertices Centroid = Divides each median in a ratio of 2:1 Orthocenter = Intersection of altitudes</p> Signup and view all the answers

    In which type of triangle is the circumcenter located on the hypotenuse?

    <p>Right triangle</p> Signup and view all the answers

    The incenter of a triangle can lie outside the triangle.

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

    List the three types of triangles mentioned in the module.

    <p>Acute, Obtuse, Right</p> Signup and view all the answers

    Study Notes

    Key Terms

    • Secant: Intersects a circle at two points.
    • Major arc: Greater than 180 degrees of a circle.
    • Minor arc: Less than 180 degrees of a circle.
    • Conjecture: Statement presumed true without proof; reliant on experience.
    • Inscribed angle: Formed by two chords with a vertex on the circle.
    • Intercepted arc: Lies within an inscribed angle; endpoints match chord endpoints.
    • Tangent: Intersects a circle at exactly one point.
    • Circumcenter: Center of a circle circumscribed around a polygon.
    • Incenter: Center of a circle inscribed within a polygon.
    • Median: Connects a vertex to the midpoint of the opposite side in a triangle.
    • Centroid: Intersection point of a triangle's medians.
    • Altitude: Perpendicular segment from a vertex to the opposite side in a triangle.
    • Kite: Quadrilateral with two congruent pairs of adjacent sides.
    • Isosceles trapezoid: A trapezoid with two congruent legs.
    • Cyclic quadrilateral: Vertices all lie on a single circle.

    Conjectures, Theorems, and Postulates

    • Conjecture: Based on knowledge and reasoning; not yet proven.
    • Theorem: Proven statement in geometry.
    • Postulate: Accepted true without proof.

    Angles and Quadrilaterals

    • Vertical angles: Non-adjacent angles formed by intersecting lines; always congruent.
    • Linear pair: Adjacent angles with noncommon sides that are opposite rays, summing to 180°.
    • Convex Quadrilaterals: Examples include trapezoids, parallelograms, rectangles, etc.
    • Concave Quadrilaterals: Have at least one angle greater than 180°.

    Trapezoids and Their Properties

    • Trapezoid: Quadrilateral with at least one pair of parallel sides.
    • Isosceles trapezoid: One pair of legs congruent; has properties distinct from other trapezoids.

    Midsegments and Cyclic Quadrilaterals

    • Midsegment: Connects midpoints of a polygon's sides; parallel to trapezoid's bases.
    • Cyclic Quadrilateral: Opposite angles sum to 180°.

    Triangle Properties

    • Exterior angle theorem: An exterior angle equals the sum of the two remote interior angles.
    • Midsegment of a triangle: Parallel to one side and measures half its length.

    Concurrency in Triangles

    • Point of concurrency: Intersection point of concurrent lines.
    • Circumcenter: Equidistant from triangle's vertices.
    • Centroid: Divides each median in a 2:1 ratio.
    • Orthocenter: Intersection of triangle altitudes.

    Points of Concurrency in Triangles

    • The characteristics vary among acute, obtuse, and right triangles regarding incenter, circumcenter, centroid, and orthocenter placements.

    Special Triangles

    • Equilateral Triangle: All sides and angles are congruent; properties of concurrency converge at one point.

    Conclusion

    • Understanding these definitions and properties is essential for solving geometric problems related to shapes, angles, and triangles.

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    Description

    Test your knowledge on essential geometry terms and concepts with this quiz. From secants to centroids, each question is designed to challenge your understanding of geometric principles. Perfect for students looking to enhance their grasp of geometry vocabulary.

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