Question

27. In the figure, ABCD is a square, and E, F, G and H are the
midpoints of the sides AB, BC, CD and DA respectively.
Prove that DMBN is a rhombus.​

Answer 1

Step-by-step explanation:

Given : ABCD is a Square

E,F,G,H are mid points

AE = BF = CG = DH

Prove = EFGH is a square

ABCD is a square , AE = BF = CG = DH

AE = EF ( E is midpoint of AB)

BF = FC ( F is midpoint of BC)

CG = GD ( G is midpoint of CD)

DH = HA ( H is midpoint of DA)

So, AF = EB = BF = FC = CG = DH = HA Prove Now in the ∆HAE and ∆FBE,

AE = BF ( Proved )

HA = EB ( Proved )

∆HAE = ∆EBF (=90°)

∆ HAE = ∆ EBF {By S.A.S. axiom of congrancy ).

Similarl ∆ HAE = ∆ EBF = ∆ FCG = GDH.

So by corresponding parts of cogreuntcy

triangles .

EF = FG = GH = HG

EFGH is a square