Question

decide whether the triangles are similar. If they are , write a similarity statement and state the reason justifying the similarity

Answer 1

I'll do the first one to get you started.

Start at point A as that is the first letter of the sequence ABC. The second letter is B so we'll record the length of segment AB, which is 4 units long.

Note how we have a segment that is also 4 units long in the other triangle; however, we won't use that one just yet. Instead, we'll go for the 2 unit segment. As it turns out, every piece of the triangle on the right side is half that of the left side triangle.

Segment ED is 2 units long. So AB and ED pair up

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BC is 8 units long; DF is 4 units long (half of BC). So BC and DF pair up

I started at A, went to B, then to C in that exact order marking the side lengths of 4 and 8 respectively. At the same time for the other triangle, I started at E, moved to D, then to F recording the side lengths 2 and 4

So A pairs up with E, B pairs with D, and C pairs with F

Therefore, triangle ABC is similar to triangle EDF. The order is very important so that the points line up and correspond in the proper manner.

I used the SSS (side side side) similarity theorem to prove the triangles similar. This theorem says that if the sides are in proportion to one another, then the triangles are similar.