### In a rectangle ABCD, E, F, G, and H are the midpoints of the four sides, what kind of shape is represented by EFGH.

- Home
- Math
- All Questions

**Answer: **Rhombus

**Step by Step Explanation: **- The following figure shows the rectangle ABCD,

Let's assume the length and breadth of the rectangle ABCD be **a** and **b** respectively. - In ΔGDH, DG = = ,

DH = = **[Since, G and H are the midpoints of the sides CD and DA respectively.]**

∠D = 90° **[Since, ABCD is a rectangle.]**

GH^{2} = DG^{2} + DH^{2} **[By the pythagorean theorem.]**

⇒ GH^{2} = ( )^{2} + ( )^{2}

Similarly, HE^{2} = EF^{2} = FG^{2} = ( )^{2} + ( )^{2}

and hence, HE^{2} = EF^{2} = FG^{2} = GH^{2},

or HE = EF = FG = GH - We know that quadrilateral with all four sides equal is rhombus. Therefore, EFGH is a
**Rhombus**.