In the given figure, ABCD and AEFG are squares.

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Solution

Q.
In the given figure, ABCD and AEFG are squares. Then

$(i) \frac{A F}{A G} = \frac{A C}{A D} (i i) \frac{A F}{A G} = \frac{A D}{A C}$

$(i i i) Δ A C F ~ Δ A D G (i v) Δ A C F ~ Δ A G D$

Choose the correct option from the following:

1 (i) and (iii) are correct

2 (ii) and (iv) are correct

3 (ii) and (iii) are correct

4 (i) and (iv) are correct

Ans.
(1)

$I n Δ A G F a n d Δ A D C$

$∠ A G F = ∠ A D C (E a c h 90 °)$

$∠ G A F = ∠ D A C (E a c h 45 °)$

$∴ Δ A G F ~ Δ A D C (B y A A s i m i l a r i t y c r i t e r i o n)$

$\Rightarrow \frac{A G}{A D} = \frac{A F}{A C} \Rightarrow \frac{A C}{A D} = \frac{A F}{A G} \dots (i)$

$a l s o, ∠ D A C = ∠ G A F (E a c h 45 °)$

$\Rightarrow ∠ D A C - ∠ G A C = ∠ G A F - ∠ G A C$

$\Rightarrow ∠ D A G = ∠ C A F a n d \frac{A C}{A D} = \frac{A F}{A G} (F r o m (i))$

$∴ Δ A C F ~ Δ A D G (B y S A S s i m i l a r i t y c r i t e r i o n)$

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