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

.

$\\ \tt\bull\rightarrowtail \dfrac{JK}{PN}=\dfrac{KL}{PM}=\dfrac{JL}{NM}$

And

$\\ \tt\bull\rightarrowtail \dfrac{JK}{JL}=\dfrac{PN}{NM}$

$\\ \tt\bull\rightarrowtail \dfrac{KL}{JL}=\dfrac{PM}{MN}$

Answer 2

Step-by-step explanation:

SOLUTION:  

The order of vertices in a similarity statement identifies the corresponding angles and sides.

Since we know that ,

we can take the corresponding angles of this statement and set them congruent to each other.

• $\longrightarrow \angle J \approx \angle N$
• $\longrightarrow \angle K \approx \angle P$

• $\longrightarrow \angle L \approx \angle M$

Then, since the corresponding sides of similar triangles are proportional to each other,

• $\longrightarrow \frac{JK}{PN} = \frac{RL}{PM}= \frac{JL}{NM}$

we can write a proportion that relates the corresponding sides to each other. 

• $\longrightarrow \frac{JK}{JL} = \frac{PN}{NM}$

• $\longrightarrow \frac{KL}{JL} = \frac{PM}{MN}$

Hence proved