Question

If there are two parallel lines $l$ and $m$ intersected by another pair of lines $p$ and $q$ as shown in the figure, then which of the following options is correct?

• A. ∆ABC $\cong$ ∆CDA
• B. ∆ABC $\cong$ ∆CAD
• C. ∆ABC $\cong$ ∆DAC
• D. ∆BAC $\cong$ ∆CDA

Answer 1

The correct option is A ∆ABC $\cong$ ∆CDA

In ∆ABC and ∆CDA,

AB = CD (Since $l\parallel m$ & $p\parallel q$, the distances AB and DC are equal)

AD = CB (Since $l\parallel m$ & $p\parallel q$, the distances AD and BC are equal)

AC = CA (common side)

Therefore, ∆ABC $\cong$ ∆CDA (by SSS congruence condition)