State the third congruence required to prove the congruence of triangles using the indicated postulate.12210203582.jpga)bar(ZY) ~= bar(JL)b)/_X ~= /_Kc)bar(KL) ~= bar(XZ)d)/_Y ~= /_L

State the third congruence required to prove the congruence of triangles using the indicated postulate.

a)$\stackrel{―}{ZY}\stackrel{\sim }{=}\stackrel{―}{JL}$
b)$\mathrm{\angle }X\stackrel{\sim }{=}\mathrm{\angle }K$
c)$\stackrel{―}{KL}\stackrel{\sim }{=}\stackrel{―}{XZ}$
d)$\mathrm{\angle }Y\stackrel{\sim }{=}\mathrm{\angle }L$

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Step 1
Given figure,

we have to state the congruence required to prove the congruence of triangles using the indicated postulate.
Step 2
It is given that both triangles are congruent by criteria of SAS
$In\mathrm{△}ZXY\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}LKJ$
$\stackrel{―}{ZX}\stackrel{\sim }{=}\stackrel{―}{KL}$
$\stackrel{―}{XY}\stackrel{\sim }{=}\stackrel{―}{JK}$
$\mathrm{\angle }X\stackrel{\sim }{=}\mathrm{\angle }K$
by criteria of SAS
$\mathrm{△}ZXY\stackrel{\sim }{=}\mathrm{△}LKJ$
so, the third congruence is $\mathrm{\angle }X\stackrel{\sim }{=}\mathrm{\angle }K$ to prove the congruence of triangles
so, option B is correct.