Question

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)\(\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{L}\)

Answer 1

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.