Question

What similarity can you write relating the three triangles in the diagram ?

Answer 1

SOLUTION

$\begin{gathered} \angle LJK\cong\angle KJN \\ \angle LKJ\cong\angle KNJ \end{gathered}$

Therefore,

$\begin{gathered} \Delta LJK\text{ \textasciitilde}\Delta KJN\text{ \lparen AA\rparen} \\ \angle KLN\cong\angle JLK \\ \angle KNL\cong\angle LKJ \\ \Rightarrow\Delta LJK\text{ \textasciitilde }\Delta LKN\text{ \lparen AA\rparen} \end{gathered}$

Hence, the answer is

$\Delta LJK\text{ \textasciitilde }\Delta KJN\text{ \textasciitilde }\Delta LKN$