Question

Are triangles DEF and LNM similar if DF = 8 and LM = 4?

Answer 1

We Cannot conclude that triangles DEF and LNM are similar if DF = 8 and LM = 4.

Solution:

Given that for two triangle DEF and LNM, DE = 8 and LM = 4.

To say that two triangles are similar the provided information is not complete.  

Two triangles DEF and LNM , will be similar if there corresponding sides are in ratio which means

$\frac{\mathrm{DE}}{\mathrm{LM}}=\frac{\mathrm{EF}}{\mathrm{NM}}=\frac{\mathrm{EF}}{\mathrm{NM}}$

But we have only information of  $\frac{\mathrm{DE}}{\mathrm{LM}}=\frac{8}{4}=2$

But do not have any information regarding two remaining ratios that are  $\frac{\mathrm{EF}}{\mathrm{NM}} \text { and } \frac{\mathrm{EF}}{\mathrm{NM}}$

Hence cannot conclude that triangles DEF and LNM similar if DF = 8 and LM = 4