Math, asked by vedsavjani, 7 months ago

ABCD is a square such that [ABCD] = 120. E, F, G, H are the midpoints of AB, BC, CD and DA respectively. What is [EFGH]?
Details and assumptions:
[PQRS] denotes the area of figure PQRS.

Answers

Answered by sakshisingh27

Step-by-step explanation:

AE = BF = CG = DH = x (say)

BE = CF = DG = AH = y (say)

In ΔAEH and ΔBEF, we have

AE = BF

∠A = ∠B

And

AH = BE

So, by SAS congruency criterion,

we have

ΔAEH ≃ ΔBFE

∠1 = ∠2 and

∠3 = ∠4

But ∠1 + ∠3 = 90°

and ∠2 + ∠A = 90°

∠1 + ∠3 + ∠2 + ∠A = 90° + 90°

∠1 + ∠4 + ∠1 + ∠4 = 180°

2(∠1 + ∠4) = 180°

∠1 + ∠4 = 90°

HEF = 90°

Similarly we have ∠F = ∠G = ∠H = 90°

Hence, EFGH is a Square.

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ABCD is a square such that [ABCD] = 120. E, F, G, H are the midpoints of AB, BC, CD and DA respectively. What is [EFGH]?Details and assumptions:[PQRS] denotes the area of figure PQRS.​

Answers

ABCD is a square such that [ABCD] = 120. E, F, G, H are the midpoints of AB, BC, CD and DA respectively. What is [EFGH]?
Details and assumptions:
[PQRS] denotes the area of figure PQRS.