Question

100 POINTS List all congruent angles and write a proportion

Answer 1

Let's check the congruency

<J~<N

<K~<P

<L~<M

Now apply Thales theorem for finding proportion

.

\begin{gathered}\\ \tt\bull\rightarrowtail \dfrac{JK}{PN}=\dfrac{KL}{PM}=\dfrac{JL}{NM}\end{gathered}

∙↣

PN

JK

=

PM

KL

=

NM

JL

And

\begin{gathered}\\ \tt\bull\rightarrowtail \dfrac{JK}{JL}=\dfrac{PN}{NM}\end{gathered}

∙↣

JL

JK

=

NM

PN

\begin{gathered}\\ \tt\bull\rightarrowtail \dfrac{KL}{JL}=\dfrac{PM}{MN}\end{gathered}

∙↣

JL

KL

=

MN

PM

Answer 2

Let's check the congruency

• <J~<N
• <K~<P
• <L~<M

Now apply Thales theorem for finding proportion

.

`\\ \tt\bull\rightarrowtail (JK)/(PN)=(KL)/(PM)=(JL)/(NM)`

And

`\\ \tt\bull\rightarrowtail (JK)/(JL)=(PN)/(NM)`

`\\ \tt\bull\rightarrowtail (KL)/(JL)=(PM)/(MN)`