Which statement cannot be true? A) Three noncollinear points...

Which statement cannot be true?
A) Three noncollinear points determine a plane.
B) Two lines intersect at exactly one point.
C) At least two lines can contain the same two points.
D) A midpoint divides a segment into two congruent segments.

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Key Concepts

Intersection of Two Lines

When two lines intersect in Euclidean geometry, they do so at exactly one point unless they are coincident (meaning they lie exactly on top of one another). This unique intersection point is a key aspect of understanding how lines interact within a plane.

Plane Determination by Noncollinear Points

In geometry, three noncollinear points determine a unique plane because they are not all on the same straight line, which means they provide enough information to define a single flat surface in space. This concept is fundamental when establishing the existence and uniqueness of a plane through given points.

Unique Line Determination by Two Points

One of the fundamental principles of geometry is that any two distinct points determine exactly one line. This means that through any two separate points, only one straight line can be drawn, which underscores the uniqueness and consistency in the construction of lines from points.

Midpoint Definition

A midpoint is defined as the point on a line segment that divides it into two congruent segments. This concept is crucial in geometry for constructing bisectors and understanding properties related to symmetry and balance within shapes.

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