Question

Determine whether the triangles are similar. If so, what are the similarity statement and the postulate or theorem used? (image attached)thank you ! :)

Answer 1

ΔOMN ~ ΔOJK; SAS

Step-by-step explanation

As we can observe in the diagram, the triangles share angle O and we have information about the sides forming that angle, so the postulate to use, in case they are similar, is SAS.

If two triangles are similar, then the ratio between corresponding sides is constant.

Let's assume that the similar triangles are triangle OMN and triangle OJK. Then, the previous statement is,

`(OM)/(OJ)=(MN)/(JK)=(ON)/(OK)`

Replace the side lengths for the first and last ratios - since we don't know the lengths of sides MN and JK,

`\begin{gathered} (30+10)/(30)=(3+1)/(3) \\ \\ (40)/(30)=(4)/(3) \\ \\ (4)/(3)=(4)/(3) \end{gathered}`

The ratio between corresponding sides is constant, 4/3. Hence, triangles OMN and OJK are similar, by SAS.