Question

$l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$ (See figure). Then

• A. $\mathrm{\Delta ABC}\cong \mathrm{\Delta ADB}$
• B. $\mathrm{\Delta ABC}\cong 2\mathrm{\Delta CDA}$
• C. $\mathrm{\Delta ABC}\cong \mathrm{\Delta CDA}$
• D. None of the above

Answer 1

The correct option is C

$\mathrm{\Delta ABC}\cong \mathrm{\Delta CDA}$

Solution:

Given: $l\left|\right|m$ and $p\left|\right|q$

In $\mathrm{\Delta ABC}$ and $\mathrm{\Delta CDA}$,

$\mathrm{AC}=\mathrm{CA}$ (Common side)

$\angle \mathrm{BAC}=\angle \mathrm{DCA}$ (Alternate interior angles, as $p\left|\right|q$)

$\angle \mathrm{BCA}=\angle \mathrm{DAC}$ (Alternate interior angles, as $l\left|\right|m$)

$\therefore \mathrm{\Delta ABC}\cong \mathrm{\Delta CDA}$ (By ASA congruence rule)

So, Option (C) is correct.