Question

Explain why the triangles are similar and find the length of segment DE. See pic

Answer 1

They are similar because they have 2 known equal angles (and therefore by deduction ALL angles are the same)

Therefore all ratios in one triangle are the same as equivalent ones in th eother

You know DG/EF = 1.25/5

SO CD/CE has the same ratio

You can therefore work out CE, and from that you get DE

Answer 2

So glad to see your response this morning. I understand your comments. I got the DG/EF ratio. But the CD/DE ratio I get 3.25/x, so how do I work out the CE?

Answer 3

well x is the value you want to find

3.25/x is the SAME ratio as dg/ef because they are equivalent parts of the similar figures

so you can work out x which is CE.

Then you know that CD = 3.25 so you can subtract hat from x to get DE

Answer 4

So do you mean this?
1.25 3.25
X
----- ------
5 X

like doing 2 ratios multiplied by each other?