NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Fill in the Blanks

Question 21

All five points are on one straight line and the four small segments are equal:

Let

\[ AB = x \]

Then

\[ BC = x,\quad CD = x,\quad DE = x \]

Build longer segments from equal parts

\[ AC = AB + BC = x + x = 2x \]

\[ AD = AB + BC + CD = x + x + x = 3x \]

\[ AE = AB + BC + CD + DE = x + x + x + x = 4x \]

(a) From the diagram, going from A to D passes through B and C:

\[ AD = AB + BC + CD = AB + (\,\underline{BC + CD}\,) \]

(b) First reach C from A, then add one more equal part to reach D:

\[ AC = AB + BC = 2x \]

\[ AD = AC + CD = AC + (\,\underline{CD}\,) \]

(c) Midpoint of \(AE\):

\[ AE = 4x \Rightarrow \text{half of } AE = 2x \]

Starting at A, after two equal parts (\(AB\) then \(BC\)) we reach C.

So, the midpoint of \(AE\) is \(\underline{C}\).

(d) Midpoint of \(CE\):

\[ CE = CD + DE = x + x = 2x \Rightarrow \text{half of } CE = x \]

From C, one equal part (\(CD\)) takes us to D.

So, the midpoint of \(CE\) is \(\underline{D}\).

(e) Compare \(AE\) with \(AB\):

\[ AE = 4x = \underline{4}\times AB \]

Hence the filled answers follow directly from adding equal segments and identifying halfway points.