Question

# 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

Congruence

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

a)$$\displaystyle\overline{{{Z}{Y}}}\stackrel{\sim}{=}\overline{{{J}{L}}}$$
b)$$\displaystyle\angle{X}\stackrel{\sim}{=}\angle{K}$$
c)$$\displaystyle\overline{{{K}{L}}}\stackrel{\sim}{=}\overline{{{X}{Z}}}$$
d)$$\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{L}$$

2021-02-22

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
$$\displaystyle{I}{n}\triangle{Z}{X}{Y}{\quad\text{and}\quad}\triangle{L}{K}{J}$$
$$\displaystyle\overline{{{Z}{X}}}\stackrel{\sim}{=}\overline{{{K}{L}}}$$
$$\displaystyle\overline{{{X}{Y}}}\stackrel{\sim}{=}\overline{{{J}{K}}}$$
$$\displaystyle\angle{X}\stackrel{\sim}{=}\angle{K}$$
by criteria of SAS
$$\displaystyle\triangle{Z}{X}{Y}\stackrel{\sim}{=}\triangle{L}{K}{J}$$
so, the third congruence is $$\displaystyle\angle{X}\stackrel{\sim}{=}\angle{K}$$ to prove the congruence of triangles
so, option B is correct.