Question

9. ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA
respectively. Such that AE = BF = CG = DH. Prove that EFGH is a square​

Answer 1

Answer:

Can you make A figure for your question

Answer 2

Answer:

☞. Given : ABCD is a square. E,F,G and H are the midpoint AB,BC,CD and DA respectively. Such that AE=BF=CG=DH

☞. To show : EFGH is a square

☞. Proof : AE=BF=CG=DH

Therefore,

BE=CF=DG=AH

☞. In trinagle AEH and triangle BFE

AE=BF (Given)

∠A=∠B (each equal to 90

AH=BE

By SAS criterion of congurency, triangle AEH is congruent to triangle BFE.

EH=BF (By CPCT)

Similarity,

EH=HG=GF=FE

Now,

∠AEH=∠BFE and ∠AHE=∠BEF

But, ∠AEH+∠AHE=90

∠BFE+∠BFE=90

∠AEH+∠AHE+∠BFE+∠BFE=90+90

∠AEH+∠BEF+∠AEH+∠BEF=90+90

2(∠AEH+∠BEF)=180

∠AEH+∠BEF=90

∠HEF=90

Similarity,

∠EFG=∠FGH=∠GHE=90

Therefore, EFGH is a square

Step-by-step explanation:

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