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Quizzes > Mathematics > Geometry

Any Two Lines Lie in Exactly One Plane? True or False Quiz

Think you can ace our geometry true or false quiz? Find out if any two lines lie in exactly one plane!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art of two lines and a plane on dark blue background promoting geometry true or false quiz

This true-or-false quiz helps you practice plane geometry: decide if any two lines lie in exactly one plane and spot cases like parallel, crossing, or skew. Use it to check gaps before a test and build confidence. For more review, try the points, lines, and planes practice and the plane shapes quiz .

True or False: Any two distinct points determine a unique line.
False
True
By Euclid's first postulate, exactly one line passes through any two distinct points. This is a foundational axiom in Euclidean geometry and underpins the definition of a straight line. For more detail, see .
True or False: Any two distinct points determine a unique plane.
False
True
Two distinct points determine a line, but infinitely many planes can contain that line. Thus there is no unique plane through just two points. See more at .
True or False: Two intersecting lines lie in exactly one plane.
False
True
If two lines intersect, they share a point and determine two directions, which uniquely define a plane. No other plane contains both lines through that intersection. More info at .
True or False: Two parallel lines lie in exactly one plane.
True
False
Parallel lines remain a constant distance apart and never meet, but exactly one plane contains both lines since they have the same directional vector. See for a proof.
True or False: Two skew lines lie in exactly one plane.
False
True
Skew lines do not intersect and are not parallel, so there is no single plane that contains both. They are distinct lines in three-dimensional space. For more, visit .
True or False: Two coincident lines lie in exactly one plane.
False
True
Coincident lines are the same line, and infinitely many planes contain that line. Hence there is not a unique plane. See .
True or False: A line and a point not on the line determine a unique plane.
False
True
A line gives one direction and a separate point off the line gives another, fixing a unique plane. This is a standard result in 3D Euclidean geometry. More at .
True or False: If two lines intersect, they share exactly one point.
True
False
By definition, intersecting lines meet at exactly one common point in Euclidean geometry unless they coincide. See .
True or False: Any two parallel lines and a point not on either line determine a unique plane.
False
True
While two parallel lines determine a plane, adding a point off that plane destroys uniqueness - no single plane can contain all three. See .
True or False: Any two lines both perpendicular to the same plane are parallel to each other.
False
True
Lines perpendicular to the same plane share the same direction normal to that plane, making them parallel. For details, see .
True or False: Any two lines perpendicular to the same line are coplanar.
True
False
In three-dimensional space, two lines both perpendicular to a given line need not lie in the same plane. They can be in skew positions. See .
True or False: Any two lines both parallel to the same plane are coplanar.
True
False
Lines parallel to a plane lie in planes parallel to that reference plane, which may be distinct, so they need not share a common plane. More at .
True or False: Two skew lines can never intersect.
True
False
By definition, skew lines are neither parallel nor intersecting - they lie in different planes. See .
True or False: If two lines are not coplanar, they are skew lines.
False
True
Non-coplanar lines in three-dimensional space that are not parallel are classified as skew lines. More at .
True or False: In three-dimensional space, the shortest distance between two skew lines is along a segment perpendicular to both lines.
True
False
The common perpendicular segment between skew lines gives the minimal distance between them. See .
True or False: If two lines lie in a plane and are not parallel, they must intersect.
True
False
Within a plane, non-parallel straight lines always intersect at one point. This is a basic property of planar geometry. See .
True or False: If a line a intersects plane P and line b is parallel to plane P, then lines a and b are skew.
True
False
Line a meets P at one point but exits P, while b never meets P; they do not intersect nor are they parallel, making them skew. See .
True or False: Given two lines that intersect, there is exactly one plane containing them.
False
True
Intersecting lines fix a unique plane since two directions sharing a common point uniquely determine a plane. More in .
True or False: In four-dimensional space, any two lines lie in exactly one plane.
True
False
In 4D, two lines can span a 3D subspace without lying in any single 2D plane, so they need not determine a unique plane. See .
True or False: Two skew lines determine a unique common perpendicular segment.
False
True
Between any pair of skew lines there is exactly one shortest segment perpendicular to both, known as the common perpendicular. Details at .
True or False: If two lines are perpendicular and lie in the same plane, they intersect.
False
True
In planar geometry, perpendicular lines must meet at a right angle, thus they intersect. See .
True or False: If two parallel lines are both perpendicular to a third line, then that third line is perpendicular to the plane containing the parallel lines.
True
False
A line perpendicular to two distinct parallel lines is perpendicular to the entire plane containing them. More at .
True or False: Two lines both intersecting two parallel planes must be parallel.
True
False
Those lines can have different directions yet each cross both planes, so they need not be parallel or intersect - they may be skew. See .
True or False: The cross product of two direction vectors of skew lines yields a vector perpendicular to both lines.
True
False
The cross product of two non-parallel vectors produces a vector orthogonal to both, used in computing distances between skew lines. See .
True or False: Two lines whose direction vectors are linearly dependent are always coplanar.
False
True
Linear dependence of direction vectors implies the lines are parallel or collinear and thus lie in some common plane. See .
True or False: In projective geometry, any two distinct lines intersect in exactly one point.
False
True
Projective geometry extends Euclidean space by adding 'points at infinity' so that all pairs of lines meet in a unique point. See .
True or False: On a sphere, any two great circles lie in a plane that passes through the sphere's center.
True
False
Great circles are the intersection of a sphere with a plane through its center. Any two great circles thus share that central plane. See .
True or False: In elliptic geometry on a sphere, any two distinct geodesics intersect in two antipodal points.
False
True
Elliptic geometry treats antipodal points as identical, so great circles meet at two antipodal points which represent a single intersection in elliptic space. See .
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Study Outcomes

  1. Understand Plane Determination by Two Lines -

    Grasp the principle that defines when any two lines lie in exactly one plane and learn to assess true or false statements about line - plane relationships.

  2. Distinguish Parallel, Intersecting, and Skew Lines -

    Identify different types of line pairs in three-dimensional space and determine which configurations result in a single shared plane.

  3. Apply True/False Evaluation Techniques -

    Develop a systematic approach to evaluating geometry statements - such as "any two lines lie in exactly one plane true false" - with precise reasoning strategies.

  4. Analyze Angles Formed by Lines and Planes -

    Interpret geometric diagrams, calculate angles and degrees resulting from line - plane intersections, and reinforce your measurement skills.

  5. Evaluate Geometric Relationships Through Proof -

    Strengthen your logical reasoning by justifying answers in the geometry true or false quiz and constructing concise proofs for each conclusion.

  6. Reinforce Plane Geometry Vocabulary -

    Memorize and correctly use key terms - such as plane, line, parallel, skew, and intersecting - to communicate geometric ideas clearly.

Cheat Sheet

  1. Plane Determination by Intersecting Lines -

    Euclid's postulate states that through any two intersecting lines there is exactly one plane that contains them (Euclid's Elements, Book I). For example, lines AB and AC uniquely determine plane ABC in 3D space, making "any two lines lie in exactly one plane true false" true when they meet at a point.

  2. Parallel Lines Define a Plane -

    Two parallel lines, like railroad tracks, never meet yet always lie in exactly one plane (MIT OpenCourseWare). In the context of "any two lines lie in exactly one plane true false," the statement holds true for parallel lines since they share a common flat surface.

  3. Skew Lines: No Single Plane -

    Skew lines are neither parallel nor intersecting and cannot be contained in any one plane (Stewart's Calculus, 8th ed.). A classic example is the top front edge and a bottom back edge of a rectangular prism - no unique plane holds them both.

  4. Angle Between Lines Using Vectors -

    When two lines intersect, the acute angle θ between them can be found by cos θ = |u·v|/(||u||·||v||) using their direction vectors u and v (Linear Algebra and Its Applications, Lay). This formula lets you compute precise degree measures in plane geometry quizzes.

  5. Key Angle Relationships -

    Recall that vertical angles are equal and that corresponding angles formed by a transversal through parallel lines sum to 180° (Columbia University Geometry Notes). A handy mnemonic is "ZIP" for "Z-angles are Parallel": when a line crosses parallels, alternate interior angles are congruent.

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