Answer:
Step-by-step explanation:
a). From the given picture,
It's given: PM = 3(LP) and QN = 3(QN)
In ΔLPQ and ΔLMN,
LM = LP + PM
= LP + 3LP
= 4(LP)
Similarly, LN = 4(LQ)
By the converse property of similar triangles,
Corresponding sides of the triangles are proportional.
Therefore, their angles will be equal in measure.
∠LPQ ≅ ∠LMN and ∠LQP ≅ ∠LNM
Line PQ will be parallel to the line MN (By Converse of corresponding angle theorem).
b). Since, ΔLPQ ~ ΔLMN their corresponding sides will be in the same ratio.
[tex]\frac{LP}{LM}=\frac{LQ}{LN}=\frac{PQ}{MN}[/tex]
[tex]\frac{LP}{LM}=\frac{PQ}{MN}[/tex]
[tex]\frac{LP}{4LP}=\frac{PQ}{MN}[/tex]
MN = 4PQ
