I and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure).

Which of the following options is correct?

Δ A B C ≅ Δ C D A

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Δ B A C ≅ Δ C D A

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Δ A B C ≅ Δ D A C

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Δ A C B ≅ Δ C D A

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Solution

The correct option is A $Δ A B C ≅ Δ C D A$
$I n Δ A B C a n d Δ C D A, ∠ B A C = ∠ D C A (A l t e r n a t e i n t e r i o r a n g l e s, a s p | | q) A C = C A (C o m m o n) ∠ B C A = ∠ D A C (A l t e r n a t e i n t e r i o r a n g l e s, a s l | | m) ∴ Δ A B C ≅ Δ C D A (B y A S A c o n g r u e n c e r u l e)$

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I and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Which of the following options is correct?

The correct option is A ΔABC≅ΔCDAInΔABC and ΔCDA,∠BAC=∠DCA (Alternate interior angles,as p||q)AC=CA(Common)∠BCA=∠DAC(Alternate interior angles,as l||m)∴ΔABC≅ΔCDA(By ASA congruence rule)

I and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure).

Which of the following options is correct?