NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Fill in the Blanks

Question 41

Why is a rhombus symmetrical about its diagonals?

First, remember: A line of symmetry is a line that divides a shape into two matching halves. If you fold the shape along this line, both halves lie exactly on top of each other.

Step 1: Name the rhombus

Let the rhombus be (ABCD).

In a rhombus, all sides are equal:

(AB = BC)

(BC = CD)

(CD = DA)

(DA = AB)

Step 2: Draw the two diagonals

Draw the line from (A) to (C). This is diagonal (AC).

Draw the line from (B) to (D). This is diagonal (BD).

Step 3: Check folding along diagonal (AC)

If you fold the rhombus along (AC), the two triangles match:

( riangle ABC) matches ( riangle ADC)

So, (AC) is a line of symmetry.

Step 4: Check folding along diagonal (BD)

If you fold the rhombus along (BD), the two triangles match:

( riangle ABD) matches ( riangle CBD)

So, (BD) is also a line of symmetry.

Important facts about rhombus diagonals

• They bisect (cut into two equal parts) each other.
• They meet at right angles: (angle AOB = 90^circ), where (O) is the intersection point.

Final Answer

A rhombus is symmetrical about its diagonals (both (AC) and (BD)).