Question

L and M are two parallel lines intersected by another pair of parallel lines P and Q . Show that angle ABC congruent angle CDA.​

Answer 1

GIVEN:-

ABCD is a parallelogram

AC is a diagonal

AB||DC and BC||AD

TO PROVE:-

$\large\sf{∆ABC\:\cong\:∆CDA}$

PROOF:-

In ∆ABC and ∆CDA

$\large\sf{\angle{BAC}=\angle{DCA}(Alternate\:angles)}$

$\large\sf{\angle{BCA}=\angle{DAC}(Alternate\:angles)}$

$\large\sf{AC=AC(common)}$

$\therefore$By ASA congruence rule,

$\large\sf{∆ABC\:\cong\:∆CDA}$