NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions
Question 78

Question. 78

Draw all the diagonals of a pentagon ABCDE and name them.

Answer:

Diagonals are: AC, AD, BD, BE, CE.

Detailed Answer with Explanation:

Definition: A diagonal joins two vertices that are not next to each other.

Write the pentagon in order: A, B, C, D, E (clockwise).
From A, skip adjacent vertices B and E. Draw to C and D ⇒ AC, AD.
From B, skip adjacent vertices A and C. Draw to D and E ⇒ BD, BE.
From C, skip adjacent vertices B and D. Draw to A and E. AC is already drawn, so add CE.
From D and E, the remaining new diagonals are already listed.

So, the diagonals are: AC, AD, BD, BE, CE.

Counting check

(inom{5}{2} = 10)

(All segments between pairs of vertices.)

Subtract sides: (10 - 5 = 5)

Therefore, a pentagon has (5) diagonals, matching our list.