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Introduction to Euclid Geometry — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsIntroduction to Euclid Geometry1 Mark
MCQ
Which of the following is a false statement?
  • A
    An infinity number of lines can be drawn to pass through a given point.
  • B
    A unique line can be drawn to pass through two given points.
  • ✓
    $\text{Ray }\overrightarrow{\text{AB}}=\text{ray}\ \overrightarrow{\text{BA}}.$
  • D
    A ray has one end point.
✓

Answer

Correct option: C.
$\text{Ray }\overrightarrow{\text{AB}}=\text{ray}\ \overrightarrow{\text{BA}}.$
Option $(a)$ is true, since we can pass an infinite number of lines through a given point.
Option $(b)$ is true, since a unique line can be drawn to pass through two given points.
Consider option $(c)$.
A ray is a line segment that extends indefinitely in one direction as shown below.
$\text{Ray }\overrightarrow{\text{AB}}=\text{ray}\ \overrightarrow{\text{BA}}$ is a false statement since clearly the lines extend indefinitely.

As shown in the above diagram, a ray has only one end-point. So, option $(d)$ is true.
Hence, the only false statement is option $(c)$.

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