Question

Help, please! In the diagram, FH = 1/3AC and 3FG = AB. What additional information is necessary to prove that ΔABC is similar to ΔFGH, using the SSS similarity theorem?

1. 2. 3. BC/GH = 3
4. BC/GH = 1/3

Answer 1

Answer: BC/GH = 3

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Step-by-step explanation:

The order of the letters is very important. This is because the order tells us how the angles pair up and that leads to telling us how the sides correspond to one another.

Note with ABC and FGH, the first and last letters are AC and FH respectively. These sides correspond. We're told that FH is 1/3 as long as AC when your teacher wrote FH = (1/3)*AC; we can solve for AC to get AC = 3*FH.

Going back to ABC and FGH, we see that the first two letters of each are AB and FG. This is another pair of corresponding sides. We're told that 3*FG = AB. So AB is three times longer than FG.

So far we can see that

• AC = 3*FH
• AB = 3*FG

The missing information we need is that BC = 3*GH. If we know this, then we can use the SSS similarity theorem to prove the triangles are similar. Note how BC are the two last letters of ABC while GH are the last two letters of FGH.

Starting with BC = 3*GH, we can divide both sides by GH and we get BC/GH = 3.