Question

in triangle abc and triangle adc are two right angled triangles on the same base ac with angle b = 90° . also ad||bc . prove that ab = cd and ab||cd

Answer 1

In triangle abc and triangle dac
<bac=<dca   (alt.angles)
<bca=<dac   (alt.angles)
ac=ac           (common)
therefore,triangle abc and adc congruent proved by aas
therefore,triangle abc and triangle dac is congruent proved by cpctc
thus,ab=cd since triagle abc and triangle dac is congruent(already proved)
and ab||cd since <bac=<dca & <bca =<dac