NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions
Question 49

Question. 49

Which points in Fig. 2.31 appear to be mid-points of the line segments? When you locate a mid-point, name the two equal line segments formed by it.

Answer:

(i) C is the mid-point of \(\overline{AB}\); segments: AC and CB.

(ii) O is the mid-point of \(\overline{AB}\); segments: AO and OB.

(iii) D is the mid-point of \(\overline{BC}\); segments: BD and DC.

Detailed Answer with Explanation:

Key idea: A mid-point divides a line segment into two equal parts.

Write this as small steps:

  • Take a segment, say \(\overline{AB}\).
  • If a point \(M\) lies on \(\overline{AB}\) and makes the two parts equal, then

\(AM = MB\)

so \(M\) is the mid-point of \(\overline{AB}\).

(i) Point \(C\) on \(\overline{AB}\)

  • From the figure, the two small segments look equal.

\(AC = CB\)

Therefore, \(C\) is the mid-point of \(\overline{AB}\).

The equal segments formed are:

\(\overline{AC}\) and \(\overline{CB}\).

(ii) Point \(O\) on \(\overline{AB}\)

  • From the figure, the two parts on both sides of \(O\) appear equal.

\(AO = OB\)

Therefore, \(O\) is the mid-point of \(\overline{AB}\).

The equal segments formed are:

\(\overline{AO}\) and \(\overline{OB}\).

(iii) Point \(D\) on \(\overline{BC}\)

  • From the figure, the two parts on both sides of \(D\) appear equal.

\(BD = DC\)

Therefore, \(D\) is the mid-point of \(\overline{BC}\).

The equal segments formed are:

\(\overline{BD}\) and \(\overline{DC}\).

Conclusion: In each case, the test is simple—check if the two smaller segments are equal. If yes, the point is a mid-point, and the names of the two equal segments are written accordingly.

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