Answer: Choice B; 3/2 goes in the box
In other words, you'll use the SAS similarity property with 3/2 as the scale factor
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Step-by-step explanation:
Choice A is not correct because we don't have enough info about all three pairs of sides.
Instead we'll go with SAS similarity. This is the idea where we'll use two pairs of sides to see if they are in the same proportion, and we'll also use the included angle between the two sides. The angles ABE and DBC are congruent as they are vertical angles. So that's where the "A" comes from in "SAS".
As for the S terms, we divide the corresponding sides like so
DB/AB = 9/6 = 3/2
BC/BE = 1.5/1 = 15/10 = 3/2
The scale factor as a fraction is 3/2, which converts to the decimal form 1.5
This says that triangle DBC has sides that are 3/2 = 1.5 times longer than corresponding sides in triangle ABE.
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If you're curious how the sides correspond, then look at the ordering of ABE and DBC. The order is important when it comes to similar triangles.
AB and DB are the first two letters of ABE and DBC respectively. So we have AB pair up with DB.
Similarly, BE and BC pair up because they are the last two letters of ABE and DBC respectively.
We divide sides of DBC over sides of ABE to get the scale factor from ABE to DBC. The scale factor must be some result larger than 1 do indicate an enlargement is going on.